<%BANNER%>

Comparison of Algorithms for Fetal ECG Extraction

xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID E20110114_AAAADS INGEST_TIME 2011-01-14T20:05:50Z PACKAGE UFE0007480_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES
FILE SIZE 1471 DFID F20110114_AACIGT ORIGIN DEPOSITOR PATH peddaneni_h_Page_23.txt GLOBAL false PRESERVATION BIT MESSAGE_DIGEST ALGORITHM MD5
fa081c3670cb2fa63466ffa7c1f6f12c
SHA-1
eb7f5fe4534c972a7d13d2e7581a291c7e56fa0e
73397 F20110114_AACIBW peddaneni_h_Page_21.jpg
060f5fd08fc4f69b1b5674d3da67bc83
1935eba8f3cd8db67ab13638ba95744ef880c825
21858 F20110114_AACILQ peddaneni_h_Page_36.pro
9d6949eac5cc49b6ce471497236ed3ef
e5edc5484e1d2904ec76c8ec207bb0ef866ed0e4
69690 F20110114_AACIGU UFE0007480_00001.mets FULL
6a0d994019bf5c7949934bb97c793dd5
1fa7be1bd52396af95a156516c039984966e9aad
1003544 F20110114_AACIBX peddaneni_h_Page_46.jp2
6297a2157ee18b16ab404babc6d16a68
4da86034e82285e2bf160f607b0263ff60212299
16216 F20110114_AACILR peddaneni_h_Page_37.pro
c54eebe2d69c4cbcea6ce63626a51ff2
307ac945904333d4a64bea9f2c9fc9289a57b22d
19262 F20110114_AACIBY peddaneni_h_Page_30.QC.jpg
b6261c4ee1447761944ec2e4962c1b89
1e5750b211afc7506a9a4577411680147603261f
45529 F20110114_AACILS peddaneni_h_Page_38.pro
522e372182ee11d085c9145e0569f8e8
a9add873788338fefdf9fea16c95de741a3417a9
1053954 F20110114_AACIBZ peddaneni_h_Page_30.tif
673d203bc72c474e2873060425cde54b
85381ff0f4da678f1e7d8c2b4d622aba9f124f1c
22820 F20110114_AACILT peddaneni_h_Page_39.pro
be3f187b1001ad504b2105c2fb7e865e
ea1b0d88141a5f4f0be34f16b67a890a21748c00
20829 F20110114_AACIGX peddaneni_h_Page_01.jpg
5e665480ebbb58ce5e4b3fc991a6f00e
908fed2677871b06f838eaf45a514ef2e079289a
31504 F20110114_AACILU peddaneni_h_Page_41.pro
13b1d36f9b92c29bbdb80a3af9680ecc
ee67901ec071dea4cd3a0a0d88af5d2b5d9c55ea
10441 F20110114_AACIGY peddaneni_h_Page_02.jpg
0662d4db2609a920d34c14403c31eb2c
32ccbec957431c8189b667820ec7a58da5190dd0
23951 F20110114_AACILV peddaneni_h_Page_42.pro
79a38f9c5d5f05e9e1069e06671a445d
65ccc6e15315781a25fdf4a873a01aeddcd3081b
27633 F20110114_AACIEA peddaneni_h_Page_40.pro
d8643050e66ab07c9bd1ea608d800583
36ebde726f084567147626077e3405eb3df13a32
8863 F20110114_AACIGZ peddaneni_h_Page_03.jpg
3c530243eedfdc4ae41e777cb3406498
5fbc2e7170daad4304d306d1e95aac80fc529d3e
21395 F20110114_AACILW peddaneni_h_Page_43.pro
61466314a8fc84b9f9fd2cabe07d85c3
fdf8978f3ec11a0fafcb99080913fbabd4d56686
7821 F20110114_AACIEB peddaneni_h_Page_10.QC.jpg
5a7b824b60817964dd1a36e3a00424c0
10930eee7f94e17491466dd4d62424869fe85864
50632 F20110114_AACILX peddaneni_h_Page_44.pro
021e3893c47e3296869d1dd9cebabde7
929d9acd77aca079785fb54ac325c6e938ee5055
5404 F20110114_AACIEC peddaneni_h_Page_28thm.jpg
833f227b77fd2ea67509dfc16507340f
f1d194e5011251d577754e77802e1c3d9ca743d5
90536 F20110114_AACIJA peddaneni_h_Page_35.jp2
8df9cdf3b98e33e9e3137c62a677be34
e34f7f8f34c19c0e0c643b35d2fe6761549975bc
22545 F20110114_AACILY peddaneni_h_Page_45.pro
5d560de7e83e486b569d43ba5294b637
1d989477414d5a25291f79afd727f8c12d7d2ef4
44555 F20110114_AACIED peddaneni_h_Page_13.pro
91d31c7cf8b2bd8f0b2e35bff6bc6762
7dd1bd8a8c40fd798da94e3b5d2dc0ce112f188e
553111 F20110114_AACIJB peddaneni_h_Page_39.jp2
f4bbd197fe3cf7a6c44b98b9cc3cfab7
72b816d980003a8b52d850d180d50086d272951b
23359 F20110114_AACILZ peddaneni_h_Page_47.pro
191a14b147d31829824970cfa39e895e
cec13dda3b44749cc6255c6e9d4170f85485b394
19923 F20110114_AACIEE peddaneni_h_Page_24.QC.jpg
e849f1623489cd4107ce00255423cdb1
ddcbaf09474c0c4b69409041080f6b337dfbadc7
882497 F20110114_AACIJC peddaneni_h_Page_43.jp2
c8855383d0c56723b9df36826271f430
d1505d1dd7b78af0fbd829f5756ee69c6d926096
50191 F20110114_AACIEF peddaneni_h_Page_14.pro
96b3340f3b06f874acdda5e320e20729
48c8d2c0ff2bdc5b2aeaa8c98a57252faae9ee53
21042 F20110114_AACIOA peddaneni_h_Page_08.QC.jpg
0bbcf4dbb112fc3389a28a538b1a1e84
297ec8827dc57f26d74146d4c4f3d7ff8f94b0e2
1051978 F20110114_AACIJD peddaneni_h_Page_44.jp2
b7e0bcd80fd9010969efce37bfc75b2c
06755e43dd05223d7a9b8e561bf49226575aad8f
F20110114_AACIEG peddaneni_h_Page_04.tif
3f308dfee0512399f576d97d2f79445f
af020af0c72ec0cfe748494d8e7b1b31a4f04668
18119 F20110114_AACIOB peddaneni_h_Page_09.QC.jpg
5036d3551e17c79dc575bb43f88ac4d5
58f180ea282cbea76fb963e839b446baa3a41a2b
879714 F20110114_AACIJE peddaneni_h_Page_45.jp2
f3af424eb97f1a98e899f17ca939dcb1
8ba6b309671b0befeca3b766a462eecf3c1ec589
5388 F20110114_AACIOC peddaneni_h_Page_09thm.jpg
926ea0796ee6ae0501eaddfacefc0668
667586418b9843a16f9dcb19757ab41f9e9fbd69
975515 F20110114_AACIJF peddaneni_h_Page_47.jp2
822055068fff07ca7c3da780e68c4fd6
2655a10ad976cef5ec9ee64ce546aca1350f6a3c
23835 F20110114_AACIEH peddaneni_h_Page_38.QC.jpg
e99d13d5587d39b75581f1f0ff97c466
8f89ea6cfa5ee3b8e1b1933b0a18edc5560f2976
21744 F20110114_AACIOD peddaneni_h_Page_11.QC.jpg
3bfc65b2a38c468800ee63a044c12331
581da99eff3343af0f2862e97e871c6ed1b61e2b
1008586 F20110114_AACIJG peddaneni_h_Page_48.jp2
507b620bab1b67937a22ec0bc2d7e0ed
692a7ef2727cffeab60a95a9ccd793bc16447976
1051986 F20110114_AACIEI peddaneni_h_Page_38.jp2
83072b401c284b6abfd7d8995e460f5b
8131573e44d8efa5af04554c20fd2978121dfe42
6085 F20110114_AACIOE peddaneni_h_Page_11thm.jpg
56c8143b1550ab0f53388006024da8c3
ec8ceb5622d486b4f4f625fb869bca08fe90f15f
108441 F20110114_AACIJH peddaneni_h_Page_50.jp2
e09c73870abd9b7eb54fa827818b6693
f7b314dbdaa7210d94ea4e73ed1587425bd8b803
47677 F20110114_AACIEJ peddaneni_h_Page_53.pro
9387adbef3e835d2a1eec9fadd435a05
b6c5ba6cb9ce36dde835f7441d04d66e76925de7
4978 F20110114_AACIOF peddaneni_h_Page_12thm.jpg
40c162ffd24c1bcf16133bfb6ff5762e
74ddaecea3814c0e1271e15c2a4e702e9920e222
103932 F20110114_AACIJI peddaneni_h_Page_53.jp2
4a16d8bda18b5657ab83779f6c6ad0b2
073aba9bae11ab40e86f604221c7674dfcca938f
963681 F20110114_AACIEK peddaneni_h_Page_41.jp2
26af6a00866d89db6d2f5307f1ebb571
55849b1df780a7beac1761bcc3df9cf4c7cf26a4
21477 F20110114_AACIOG peddaneni_h_Page_13.QC.jpg
1763d449cb50fabde013162bbdf74e91
a4057d713439d0280136d615b5a055fe5aa0b287
109280 F20110114_AACIJJ peddaneni_h_Page_55.jp2
3d4df33ef0e6cb11c0d95dfd817b5e34
6b63e99cbf8e4e47c5ca1ca364b24a8cc4709e94
16462 F20110114_AACIEL peddaneni_h_Page_45.QC.jpg
eae589925ac3288533cc3b554572c14d
d30371d011b83b422963de6f8da491fd2888c17b
24139 F20110114_AACIOH peddaneni_h_Page_14.QC.jpg
52dff1935af6fc679e1028829c5052c7
84cf888401574aeb80c3176f4b429b5f1e85b7a1
127641 F20110114_AACIJK peddaneni_h_Page_56.jp2
cbb93be12ebadd507d28520c822b1892
61b899abe5b4cb4974180ce134c43ed01ab806cc
1833 F20110114_AACIEM peddaneni_h_Page_11.txt
2b0fcf87529001bfca018faa70b91d26
a00da200752082dda7d58e57cee67f69624dfc2f
38541 F20110114_AACIJL peddaneni_h_Page_58.jp2
dfbff6f836162aa94ceccafe3eb305a6
b5e635b459e2bad5cc9fd85c8f9d04165515c162
4881 F20110114_AACIEN peddaneni_h_Page_51thm.jpg
a1b15842bc1345a6dddbe11861ee9af9
5f1fa3292a7f6ab5103e1946bdad02ea8f94f39f
6641 F20110114_AACIOI peddaneni_h_Page_14thm.jpg
8a8a1add20382f1740c62ce0693f1cda
cc06fcf74fa26034732521c6887bc15dbec2a75f
2783 F20110114_AACIEO peddaneni_h_Page_03.QC.jpg
4481e0b72081dcd19573fc1d2c5b3453
b8d01f6735510d8c91f64a7031c33afe5a9bd679
6880 F20110114_AACIOJ peddaneni_h_Page_16thm.jpg
9ac3ab745d33bd4f9a0c8fb72570c4c9
41d1dab91354444f1027d93963f2dfe35ea119e3
F20110114_AACIJM peddaneni_h_Page_02.tif
1951f98c8e9aed87dff19f67d6fde8dc
bf65a9e8e7e8a149d49e6009971427a220b9b83a
23385 F20110114_AACIEP peddaneni_h_Page_10.jpg
37505176a1d2147ae1cca9779d21bfdd
64ba40949e93bf525ad3c90e749d389a369ab7eb
19990 F20110114_AACIOK peddaneni_h_Page_17.QC.jpg
2efef09ea7ac1151e91c7a8551270b2a
6e319f609b99ea35e89c16880c91c53cce6f1036
F20110114_AACIJN peddaneni_h_Page_03.tif
e42728f42ab22ab6daf8fdf8d7f62e13
67038195e47ff6fbe371926bdbecacde75266d3d
43721 F20110114_AACIEQ peddaneni_h_Page_11.pro
e3c3f48cf83f6b1d344e2f9a5f8504bf
67e12e37e7f6c274fe66f777f95c381dbc064282
1559 F20110114_AACIOL peddaneni_h_Page_18thm.jpg
719e0010b24fada78c28f828e214f6f4
30aeb22d2826d2cb6074d9f3a2620582564b9155
25271604 F20110114_AACIJO peddaneni_h_Page_05.tif
c6b7924adc07ad7e295d1eda645489aa
45ab9295413de0f5cfe24b98ba22491575bee7bc
44217 F20110114_AACIER peddaneni_h_Page_54.jpg
3e9b518bafccc7ccf17f4703e7db97d0
72a982b7b40c355c1b42c02c8caa6272beb2d265
6000 F20110114_AACIOM peddaneni_h_Page_19thm.jpg
88aae25e5af8850417a1da919fea7aad
af0a4cf8413036fddf3c4c3a5bd5da83d36caa30
F20110114_AACIJP peddaneni_h_Page_06.tif
2d0e7cea1844e9b55226ba8c526eb058
dde4b2195936bf58fbbd2c7a218db0be6b08d8fd
F20110114_AACIES peddaneni_h_Page_15.tif
492b64d6c562b2f7142033c4244e75ad
226ea3044a5224fcdd8f93b55e577152e55aa376
19172 F20110114_AACION peddaneni_h_Page_20.QC.jpg
42f219c0a4d84544a7e7ef2cf39a69ed
139be9e1c8aed53553ab8ceed6d8c1f9ee032fe2
F20110114_AACIJQ peddaneni_h_Page_07.tif
4a43453f3bf31764d788727eaeb5137a
72312a2237e22e4a3685d7b63f6dac3966d621c0
1587 F20110114_AACIET peddaneni_h_Page_52.txt
cfa37655840b71e2261bf0c6ea22ca12
40d321da7470a690b03fb760187c2318bf7061f1
5678 F20110114_AACIOO peddaneni_h_Page_20thm.jpg
0aaf03c3d786e8049273b331229d1d45
e89852e8143183a5b0094675fe7fdc3e8bbbc845
F20110114_AACIJR peddaneni_h_Page_08.tif
8177143a781b601295b7f72af7ac62db
02aac48a1b25f17e12753baea20918d1c30a66e8
44220 F20110114_AACIEU peddaneni_h_Page_04.jpg
c04b59e0ab7b80dee654d1cfb8141cab
13be955dd315e1d6531940ca23c2bc209d9d9d5c
16309 F20110114_AACIOP peddaneni_h_Page_22.QC.jpg
4dc02cf845d8cb2b99506dc5ee2eaebb
13cfd7576e11a27630e0ea5fc93945931c834fad
F20110114_AACIJS peddaneni_h_Page_10.tif
5a85a43cea33058868069ce928b9479a
12306f0a9ad7dd5506c15e9721b070578911ffd4
28513 F20110114_AACIEV peddaneni_h_Page_10.jp2
efb205812e7bb2de9f0ca5d16dee2b4c
9641c307e4caa61a61eab94237ac81cf2cddf66d
4951 F20110114_AACIOQ peddaneni_h_Page_23thm.jpg
c2b3987837c2b0ed21ffe6b461b7f92c
573c774a58a12d029fe5272d69925ec4a66104d6
F20110114_AACIJT peddaneni_h_Page_12.tif
d86a6d151fcd690f0e6064d7b2934322
916de7cff7c94349a6e1698a40d2fe783f9e5958
16271 F20110114_AACIEW peddaneni_h_Page_51.QC.jpg
077ce552fe6ccc7a084c2c685fe0a7a7
148acdd7997b3daff4b999850d64cd17e3a5466a
F20110114_AACIJU peddaneni_h_Page_13.tif
803d69b581e52df16256e8a147ad7e0a
d99e35ec6fc7aaff91f5aa9e762bbcf6feea2116
6914 F20110114_AACIEX peddaneni_h_Page_15thm.jpg
cd14169e662f880e6e6260c33a1be913
644551226760e01534612cb2a0ec5cdf4633ed87
15567 F20110114_AACIOR peddaneni_h_Page_25.QC.jpg
8b6fd0f58df07f21fd05850ccc521cb8
beeb3fc8c624a6ca99ca2163d98055c6957a41e2
F20110114_AACIJV peddaneni_h_Page_14.tif
7150f9a8826884366552ffb4a1aabd70
0b81df1e8534ea1491d4095d0b7be3c022d8bc71
9862 F20110114_AACICA peddaneni_h_Page_58.QC.jpg
8d289fd0860c0a2d0503b9d0f04651cc
9842e7047b3cf17de1c2453f228b8f4f4f7dc996
49922 F20110114_AACIEY peddaneni_h_Page_50.pro
71cd70fb04452c385809aa732b9280db
5dfb3fa27b984ecef7029977ec0db03b03081e85
20683 F20110114_AACIOS peddaneni_h_Page_27.QC.jpg
a61c42d3253d9e7f5606ba941c63ee80
560788a669e76d799f65993dba54859291a2f360
F20110114_AACIJW peddaneni_h_Page_17.tif
fd53473ab88c0f08b9cf8fd739faab14
0ff35d996039f00e4bf504e638866c542cd52ece
1051976 F20110114_AACICB peddaneni_h_Page_08.jp2
97b5ade8cbc41dd0979ff117684ef170
7c2a60724e2fa97ab054d69605fdd3ce4416995f
73418 F20110114_AACIEZ peddaneni_h_Page_50.jpg
bbbdfad5b4efcb0ceebc6f710ba65389
426012ca802366bbb29fb35c86d3d785bbc6a1ae
15927 F20110114_AACIOT peddaneni_h_Page_28.QC.jpg
91b09b6d6acea8a6bbc145644ee3a924
28c4ab7360d44155055ffa6d8977f71d4717c7a1
F20110114_AACIJX peddaneni_h_Page_19.tif
909e61c13268d454dcdee6054dc6cc94
5e80aabac0996a9670c66afe9cf3e1dbadf682b4
5947 F20110114_AACICC peddaneni_h_Page_24thm.jpg
181547aed6cc1f284c60f6707e690d20
3b076ce63ae246307ce895f92ef419bb25ae7f5e
18454 F20110114_AACIOU peddaneni_h_Page_29.QC.jpg
8a5fc02855d4b5b58d6dcf330a8bb454
b1439f9093b495f04a87982a8a8d2bf531b7e9d2
F20110114_AACIJY peddaneni_h_Page_20.tif
20ea611a218ba408deb982503d1c9c72
4d024b194cbaeedef142c029645f0effe9342899
76044 F20110114_AACICD peddaneni_h_Page_15.jpg
d9c1f0d2fc981a981fa1f04b5cb358ef
98deb319cb07c74c71f4482a93575576f0f2e60f
5765 F20110114_AACIOV peddaneni_h_Page_30thm.jpg
e5b5d43a9e8d769a8c2b8306d1374d0c
6bc7f678a27679a6177074b78524eaffe387b07b
F20110114_AACIHA peddaneni_h_Page_07.jpg
9c4795d4283da7b1e81a031209fb8a49
c2f47461443d2d23cfe5b7606957cdb68273d138
F20110114_AACIJZ peddaneni_h_Page_23.tif
84295532e86c97bab18c8c464dc96881
49e3f6f47fa3837c2827a0f58656a89fe011e2e8
15727 F20110114_AACICE peddaneni_h_Page_12.QC.jpg
15c5a24781805c1cfb2da5059e0c7311
1f02b3cca683210c8597d02c737799d406a4bfd1
14234 F20110114_AACIOW peddaneni_h_Page_31.QC.jpg
453b18afd293485515e0cb231b3736a6
404540203c16effba4281120cce0b82dcc7fdad2
75194 F20110114_AACIHB peddaneni_h_Page_08.jpg
14ff17f1d260544bf86ce5632177520a
eaabc12bf48a62bfbb391199431f20ac8dc7382e
12131 F20110114_AACIOX peddaneni_h_Page_32.QC.jpg
1fe78c89880ac9692a56478335ba0359
4161747fb08505b05957dc47d38f96759cfc7ded
65147 F20110114_AACIHC peddaneni_h_Page_11.jpg
a5b9f0a741b4a52556d6d33b796fbb29
3bf22d6178bfffdd04bc306fbeee9cd14f6e3e7e
860726 F20110114_AACICF peddaneni_h_Page_42.jp2
af2b74a4f4caac71d021a9841a5c741b
5b0032768e1a4d76c56883e8da138e4c9c6bbd41
24426 F20110114_AACIMA peddaneni_h_Page_48.pro
35b2cdda5ef1b287001babeaa10a9a94
5ea04a7d7f6c88b695f6dae695bc7a0f2afba04f
18930 F20110114_AACIOY peddaneni_h_Page_34.QC.jpg
dc88b418f198b5f93fd0c9744e19ab1d
cbd8e142de6286b1fe7bbe994f7bf7fd6843b510
50731 F20110114_AACIHD peddaneni_h_Page_12.jpg
3aa18bdad9172b4ff84bd4b20c48dde3
99d6124e1138de0b019585063c70359ab22a58b8
27012 F20110114_AACICG peddaneni_h_Page_12.pro
f9344a6bc27c359c7981e2abc9fcf431
637be08b4ef14ff21161ba3a5ffc1b84f2074773
22520 F20110114_AACIMB peddaneni_h_Page_51.pro
fe1304ec7ae46c473d17595a477a5682
02b8d702e3543b4bc9e34d2914c133d93ce7d725
F20110114_AACIOZ peddaneni_h_Page_35.QC.jpg
ff2a17814d070dcb9dc4a13d90858f66
a87c7e7065a5895f0312e80521290b17708eeba7
65325 F20110114_AACIHE peddaneni_h_Page_13.jpg
2af305aac638ad6a052ff5c7cee8f668
6b7b72c1ee1f0a157d187292a55b977138abbfcf
49613 F20110114_AACICH peddaneni_h_Page_47.jpg
1d0b86cd09f1bf964931d4a7b1e7319a
07af6d935aaf3fc6206ace8761b20239c789bc4f
27469 F20110114_AACIMC peddaneni_h_Page_54.pro
cbc675d83a8d25781ea7ee2c7fd00406
8ce8d55785265def60dbfe9316051522f9edced2
73622 F20110114_AACIHF peddaneni_h_Page_14.jpg
0648facc8dedc131a710b663a59b0d36
3362c433443d048e1c897de7112e4528a9559dc2
F20110114_AACICI peddaneni_h_Page_53.tif
fb95d4fbd9c5b6d6f53999d500834638
a094c6a43e92e196c10f9bc9f15418124e4ab16d
50983 F20110114_AACIMD peddaneni_h_Page_55.pro
e55bf6e43bc5f9ff7563698ad1ab259c
ac0f2efabeddecabc79a929895c83bf9c25fe312
73687 F20110114_AACIHG peddaneni_h_Page_16.jpg
592148d243615d1d4dbfba2a151b4a63
fe75f8ddc487387d6c58f497a496b288af6443c8
F20110114_AACICJ peddaneni_h_Page_58.tif
2e7d04325eca405010b4a46a630d8a1c
035fdfe828df225517e30b289701ed51c72d62f2
60213 F20110114_AACIME peddaneni_h_Page_56.pro
404f017ae7ec121eda6e53125a950c9b
cb765e641b7bf06a9341987361dc6c23c5edf105
62217 F20110114_AACIHH peddaneni_h_Page_17.jpg
95acef3421cdfca098ee36313efeda0d
32d2739b5506281b0b5db36d669408fe594c9755
83972 F20110114_AACICK peddaneni_h_Page_26.jp2
edff47bce1ddcabf53e7966ce769259d
69139cd9a799bc70beaa682576d9094e62a77338
398 F20110114_AACIMF peddaneni_h_Page_01.txt
fbbacce2be700e8516ce9ec3fac68c94
309437bc90ed1508f2ed952231b231a47826eaaa
11629 F20110114_AACIHI peddaneni_h_Page_18.jpg
2d103686ebe33b13cdec791c0628baf0
3911eac29223f38b0b7f99205d9e1a4792aa7493
1747 F20110114_AACICL peddaneni_h_Page_24.txt
6a297909bd971bf6ff8106c56b59bc58
3e18c8d4287c53cf2425084c444e202e2b8981ae
1117 F20110114_AACIMG peddaneni_h_Page_04.txt
15a318fa47f24bdc83f927dd4af6b8ff
ebb968291f16ab4ccec8492c8c88e1c5a50c730b
55163 F20110114_AACIHJ peddaneni_h_Page_20.jpg
dde220414f8e55b6322e1949728cf41c
29b25873f58d7b7402d6bad018c08cdf08ca3764
5082 F20110114_AACICM peddaneni_h_Page_22thm.jpg
824b8d589a967d652f567a4e7dfcfdce
6b989c301023fea209aeab44c4bfb1322254f9e9
2843 F20110114_AACIMH peddaneni_h_Page_05.txt
5e81bde64f35844297af6ab47d8587f8
77b92bd83c0db339f49a2909d4968d96cf27569f
F20110114_AACICN peddaneni_h_Page_01.tif
f6cdf50c212c01f272ffce24b10c2929
775e392161a154c82529c03b82f9b7ddc0c34f5d
139 F20110114_AACIMI peddaneni_h_Page_06.txt
7e025ba27bfdcdb009fa2aae3bc20545
da00fd34485f1f36842a25bff259e6a9745a41ec
50645 F20110114_AACIHK peddaneni_h_Page_22.jpg
779a898952e183e31a55ceb4a7de2386
cf033c02231dcb332b3e233361a8f5bab6da024d
22 F20110114_AACICO processing.instr
f229bf29a64a144b707cf692d8ae638d
d08cc9afac3a6cf8ea356117be05b7e63a546373
646 F20110114_AACIMJ peddaneni_h_Page_07.txt
248228e6446b43d3ef5d692ceeb3fb1a
4cf7cf03631a10e647e62a49efb37c217a4078db
44911 F20110114_AACIHL peddaneni_h_Page_23.jpg
c075647ef2a16c2b2cff05e68394d9a0
af38570d53db139a6a594412db6e28db4e3cfe61
21735 F20110114_AACICP peddaneni_h_Page_33.QC.jpg
816965ffbb76aa70db1b743093c5d200
74fb1ce8e976dd6339b079cecc5a8cdaca743374
480 F20110114_AACIMK peddaneni_h_Page_10.txt
5b5c5963f1cdf413ffea1dd28c65963b
6dc283352065b6722dd4ed048062349a49040554
59850 F20110114_AACIHM peddaneni_h_Page_24.jpg
a706db8106dc384260eac3fbefa1f772
210c40aff1551d144fc418d4f1d1079cb81a83e9
6254 F20110114_AACICQ peddaneni_h_Page_55thm.jpg
61a324b34dd1e3f76a20b699ee3cc93a
b53d5c19ca3f1dd5817f021e419ae276f23c133d
1108 F20110114_AACIML peddaneni_h_Page_12.txt
324405bfc4bc98e2a81541decabd2f95
d60f1f619a55dc346646f97b135e15af87e54a31
46190 F20110114_AACIHN peddaneni_h_Page_25.jpg
accc4f6af5d3abc04f6d328557ff0922
8003d0d9f50876bcdc358449716cd7b0489d7258
48565 F20110114_AACICR peddaneni_h_Page_36.jp2
8b51452cbc6ec45f4b2044241f63f514
370336e29aaf69e9c1bf55ca0272d9597c03a28b
1806 F20110114_AACIMM peddaneni_h_Page_13.txt
ba932e11a37592d9d3c844172961f5c1
fb03a4bdd375005b802c03f62316d6d4daadccad
64150 F20110114_AACIHO peddaneni_h_Page_27.jpg
59df91f5a7384267d26bbf8ee6d2a53f
3b6b1f3bb25ee3d4e6a340c1d7db95a5ee43a6a4
1751 F20110114_AACICS peddaneni_h_Page_21.txt
1ac2e34bb3fcf34b7846faf7e9a177cf
6b37094825256e8bd212bf671b3ef04ca215d806
1976 F20110114_AACIMN peddaneni_h_Page_14.txt
054cd979c9b4987a2070fcfe3d5cbe8d
fd5f223e667582e566d9c89180ffa22350930291
48355 F20110114_AACIHP peddaneni_h_Page_28.jpg
7919c12c1b00940fb5d28ad1a6ca4ae9
415631b004c42dd4192738ae3b64f233c032f582
29196 F20110114_AACICT peddaneni_h_Page_23.pro
37e1d2e11d9de3dad23e566e5cd2eab3
c9f91e190c1ad65be6e9afa5a0db7f4954808096
1956 F20110114_AACIMO peddaneni_h_Page_16.txt
1695d010302b3dd5bf7c4b0e64caeb42
e8192e31d48dd7093cd8ad09a2f5bb0793f12bf1
55383 F20110114_AACIHQ peddaneni_h_Page_29.jpg
5eafd112658204ee8a8977bdbd8661eb
34b61ea48506b8c84df0b4752d8771ca0eda3ed4
23970 F20110114_AACICU peddaneni_h_Page_16.QC.jpg
df09d302c7a9fe611949ccc893ed6338
c5765fa413a7ef8196d848590d7192898b8e8064
39639 F20110114_AACIHR peddaneni_h_Page_32.jpg
4aca5055c10721a2be2ed054dac799df
6b2c92976d092a11822ae85e105805a8494d2d69
2471 F20110114_AACICV peddaneni_h_Page_10thm.jpg
d499925f4437405cef742359f2102111
118de7f645cccdb6e336495bbeb66a2a62995d18
1758 F20110114_AACIMP peddaneni_h_Page_17.txt
572108f3b146ed2b062da14099d206a6
d26de95628cce154da189c7428bb493db3a6f38d
61334 F20110114_AACIHS peddaneni_h_Page_35.jpg
477d8b29686aa98b802f6182a5bec79b
2182163f6f158e765e0a7de605dedbe19bb00b93
600606 F20110114_AACICW peddaneni_h_Page_40.jp2
5d7a28c83bcc388f4158c7634e41b261
402e5359048d2d109c3eecbd2e7e7c925c7ae1d4
162 F20110114_AACIMQ peddaneni_h_Page_18.txt
f3cef99c0a5e1243ffe7c14d8114c108
0091220a1e960cfe88480f5bfb570038000f0c13
35414 F20110114_AACIHT peddaneni_h_Page_36.jpg
763fce6add70af21aac038c4a6309f22
407b48cc87aaf1bcfdfaedc68a4c8c4028bccbac
F20110114_AACIMR peddaneni_h_Page_19.txt
09ec1e5e4a01cfcf4756cfe7c2aa4978
671c0a53f38070d7d8874944e74f4a60b3b2eac9
37850 F20110114_AACIHU peddaneni_h_Page_37.jpg
8837249fcad9c1154a201f1db1b53efd
9f4eabb2dc4a1498d2c6d51addc810bfa5913ef6
14611 F20110114_AACICX peddaneni_h_Page_23.QC.jpg
e86e89584ef87e3c72e5bc4810e71ff2
d0034720f70826bb4c54d349567dcbc79f5fad1b
1709 F20110114_AACIMS peddaneni_h_Page_20.txt
a361c661e6d0c01fd1d21d15989462ad
40baa47465edc7b615915975c1e35773e1b8cb84
79837 F20110114_AACIHV peddaneni_h_Page_38.jpg
047546280d34e0d12c83b6a86b91d6ea
e97b05070ddb4b2c53af20bf9d3d646cb252d031
3065 F20110114_AACICY peddaneni_h_Page_03.jp2
0a42b95143247da9eae2ab3976943d4a
edd0e8083df36443332997622619e23ff9eb0934
1682 F20110114_AACIMT peddaneni_h_Page_22.txt
4eeeea6e3e8fd2ba5d3c3b84c68d797a
33f618c94b921ab18d9af6e93d43fbaefb69c2b1
40658 F20110114_AACIHW peddaneni_h_Page_39.jpg
27e21903f8e04f0029059bec65058634
57e97fd205f6afe2739b5cf397df26065db28eee
13150 F20110114_AACICZ peddaneni_h_Page_47.QC.jpg
8fb2b20c4b8b4a1fc719336b2bb43437
16d07e5b441f166d48cd58063d812b5e472452b5
1532 F20110114_AACIMU peddaneni_h_Page_25.txt
1a6581bec1b76ecf4eb424105f03f92c
f925b768ca10b5ef14dfb708f07b803ec6dd7456
47584 F20110114_AACIHX peddaneni_h_Page_42.jpg
427d270239d2cd3f45a820e3cea10b83
3d9449b6da456eb0a53948786c991fd0f80b604f
1609 F20110114_AACIMV peddaneni_h_Page_26.txt
9fb43c59c2ab0badf48cf6a968dd0d66
8e6a06a8bf9444ce993e29a72c721db4cdc7ba88
81074 F20110114_AACIFA peddaneni_h_Page_09.jp2
0473cb97641f2ea94515472071b2096b
cefedba80f39047972e601b9a7178792f2bc74ab
48523 F20110114_AACIHY peddaneni_h_Page_43.jpg
8588ccb53ec7f676d184e843f97315f0
2ee3a5c74d0d746e8c4161650b20bf651764377d
1662 F20110114_AACIMW peddaneni_h_Page_28.txt
8f53f688247655941198973665ef425c
e0b63e1385785bcaab57808bbf5e61f0621fe822
11036 F20110114_AACIFB peddaneni_h_Page_37.QC.jpg
185f67d92b26c66deac3e8be785d28d0
65008445c9e5b1e0123de05e60a072ea8e95c681
82344 F20110114_AACIHZ peddaneni_h_Page_44.jpg
47079a12397918cfa352f1fbd609eaba
d7f2bbdc794fbd395119edc9a1c4b7ec58b4e988
F20110114_AACIMX peddaneni_h_Page_30.txt
e0c98af51f97f8cbb9d05b181f48b827
eddee14747f2f61d28732adc73ee3cc45296dbfe
22082 F20110114_AACIFC peddaneni_h_Page_21.QC.jpg
bc919d08c90de3099af52d56b4a3237a
2c92daf695979055b447af93c67e9faa6e3ef9a6
1036 F20110114_AACIMY peddaneni_h_Page_31.txt
3cc81c66f6cdbb5e1d38a0ddc1634c62
f37e73e2eef9530ece633655b6635c534754d867
9429 F20110114_AACIFD peddaneni_h_Page_18.jp2
e232fa9159eaef70cfbd31c500aa03e4
ea00f15cb5bdb493d34faba0f1d377c2831403a7
F20110114_AACIKA peddaneni_h_Page_25.tif
d2817e570d80131e34d06aa9020acf58
c7a7ae327e2916e141708cd7c26d794e0f0fb9e4
1856 F20110114_AACIMZ peddaneni_h_Page_33.txt
5f912d553484366816ac7fd38dee2711
1ba7aa6fe61ebbdeeb617b39680ecfbbd1b9aada
F20110114_AACIFE peddaneni_h_Page_21.tif
866b212dfd1625b14144d40fd97c4d52
40a261986e2142716137c7e3567568eb995b5a1c
F20110114_AACIKB peddaneni_h_Page_27.tif
f5cac511d5998aa4f7c244c0303fc2ab
5e16bf13fe65c8359800f8abc6623baf1eba0418
1771 F20110114_AACIFF peddaneni_h_Page_27.txt
de4aba22722b0d5494cda3cb51499878
26b6730567aef37b7f4db4239df27c436ebdc872
F20110114_AACIKC peddaneni_h_Page_29.tif
ad7771c9a5b2f3cc02573cede9d33b49
49cbeecd603c7d6faea0cc52c2164f2f290bd4ee
1585 F20110114_AACIFG peddaneni_h_Page_09.txt
793c0e9f84fe2a26866777ec9b099c4e
a4e2a3a447d05c8d9b6dfa9c602f7308d8f153ba
6242 F20110114_AACIPA peddaneni_h_Page_35thm.jpg
c6ef05f23e43e0ecca297b3a553acf19
e6e0fbd373c77375e3fd3ef1ed995f114cc330c9
F20110114_AACIKD peddaneni_h_Page_33.tif
1ee2b815c9b11d44288275d403f8041f
05570aa51304c37e8c2e9c2db5242457124a77e9
115 F20110114_AACIFH peddaneni_h_Page_02.txt
5cd90c0eb81c396d9e9dee1dfd095fac
b93bfa923b415d06a1257ac0d5a95e1461a404eb
11817 F20110114_AACIPB peddaneni_h_Page_36.QC.jpg
9bdd21e8c9c35c44bd216dc8693aec7f
7f70fc83432c353773db715c2ade77d9090b4cc8
3675 F20110114_AACIAJ peddaneni_h_Page_48thm.jpg
4b965a1b5566a26621acee05dffba960
aa55d0eee5ff5520d92ac73b8f08cab6e47ff8da
F20110114_AACIKE peddaneni_h_Page_34.tif
c6f243c8de9989babc77bc24b41dfbec
10de5eb72b238fe0b528f210d56bbb66ecf13f9a
3770 F20110114_AACIPC peddaneni_h_Page_36thm.jpg
5fbf3dfb42fa67958083fd6e2d792485
e2b63d1c8a7436a3387ee4d8918a7720606169b6
1034 F20110114_AACIAK peddaneni_h_Page_36.txt
1280fc2584fdf89f561a4cd88c5f44f0
3b1dd16bb1d05717862fb98d0bf31a7fc393ae64
F20110114_AACIKF peddaneni_h_Page_35.tif
fc5d3f611667c15084639ab25b56211a
07911bf267618711b1d8537f7dc544d99c111455
1051969 F20110114_AACIFI peddaneni_h_Page_49.jp2
d926f1faf64e2ed2b155cb89a8019301
9bca6486b3f6344fab85566aede277a8ded86671
3524 F20110114_AACIPD peddaneni_h_Page_37thm.jpg
1fd68911e32678abcdfecbd449eac0b8
a36820a39b65deae3e9bd2ca18b59ae8c5a54467
96420 F20110114_AACIAL peddaneni_h_Page_13.jp2
a9ad74073a5eb855e36052a73069d37a
2916a0cd7aa18506a4a28244019e4e7e67b207b1
F20110114_AACIKG peddaneni_h_Page_36.tif
e0e7f923d81440cad290b0d9ea851d7a
ff48ee6bba2ed8452cffef18ff4d57ec86e9b358
52858 F20110114_AACIFJ peddaneni_h_Page_45.jpg
bf7e76b6b8db1a5d401bfc3a8f361701
f93fed71eedb8734ec75a8b318b13782e5d0ea56
6534 F20110114_AACIPE peddaneni_h_Page_38thm.jpg
02ec6beb877f303b0ab77d5af3d5b77e
57df7fa6402401c39db4e00d0fd7c204b5997247
3427 F20110114_AACIAM peddaneni_h_Page_06.pro
08bf91819c730a68cc8d8c0947933277
0b13c30095fdb34fd7948e960b666b20c4ae144a
F20110114_AACIKH peddaneni_h_Page_37.tif
c00f7a8c0d66e207df8c956d631eb4f5
33fcdeb0ab6894b499e2910bda0bd8abfcc18b75
6101 F20110114_AACIFK peddaneni_h_Page_13thm.jpg
3509e75a3fe56f0e4a7d7007b3ca1e6c
829f59dceabe3622785981cb3eecb543f1674479
4314 F20110114_AACIPF peddaneni_h_Page_39thm.jpg
2c30364d9ff423aea0373280a9b8fe17
270542825e7cf513e68e6b3672b86c810cd1bf10
1229 F20110114_AACIAN peddaneni_h_Page_02.pro
297f63e00c3eb0c7a2e0be1d0da0ec6c
89c253c520a960bccf088c5233bf4b5f6694c2d0
F20110114_AACIKI peddaneni_h_Page_38.tif
ca790fa82d00150657d6eec93139cc47
0c9d45e6326df77f8052fce43ba25d1d50eaadc0
56761 F20110114_AACIFL peddaneni_h_Page_30.jpg
0e1bc1f38221ea2989a74187704744f6
5955d39fa98f681e0ef455c494fd7f4b783b068d
14512 F20110114_AACIPG peddaneni_h_Page_40.QC.jpg
64968bd77f7b0efe3a582975d1696d4b
533c752b76201b20ff78719b030a84177ad9716c
62289 F20110114_AACIAO peddaneni_h_Page_54.jp2
8f92e0f4fca7ebd15f29080991d145bf
6a5d2d48cbc341e485f77288341e76febe1ff868
F20110114_AACIKJ peddaneni_h_Page_40.tif
d38e7d0dfa9a3a846c8a56c316284c4b
42b15e7519a731b15ad175c34fd1e8b53989d4ed
3598 F20110114_AACIFM peddaneni_h_Page_46thm.jpg
4551529aba10409f5f5508b1012605d3
d8ba832a4ec987f1d1ebcae7b2846131e4058a6e
4472 F20110114_AACIPH peddaneni_h_Page_40thm.jpg
bbcfde5528339a40e06908a09450e911
ee90408c9328cbab12c1cc842b6b74963421e2aa
18972 F20110114_AACIAP peddaneni_h_Page_26.QC.jpg
79aa5a2218b8804cda86d0d7139a5121
5c542c3f74c3e42373dda92573c6a4b552f81764
F20110114_AACIKK peddaneni_h_Page_41.tif
5ec88aed1c7fdf2bb8765265e2616122
0a7a909be06525737fb27bb71f971016d34d1bf1
2278 F20110114_AACIFN peddaneni_h_Page_07thm.jpg
8aaa903eaba512a3970d79b449e5c4e1
9a96331091d8d97d98f5c69200ba143619ab0c72
18691 F20110114_AACIPI peddaneni_h_Page_41.QC.jpg
77d10b5aff5325f0dc28a9393bc73bb7
89a92d70d79c2b39b62272e873d95d8a330d156f
5778 F20110114_AACIAQ peddaneni_h_Page_29thm.jpg
25cd02d45d1943f33e3477d7714f2903
355fb8fbb2745547eeab877eca734a5d0268bd1d
F20110114_AACIKL peddaneni_h_Page_43.tif
fa1f4fb425e0027e6b79143f1146c6fe
2010f445237506dad692a8d1f3710ad35ee3185e
18702 F20110114_AACIFO peddaneni_h_Page_46.pro
2cbd07b70693b4ef37778da650b44109
cdb308ed7e86afca3dec14ae4cf4c55bac8076ef
5511 F20110114_AACIPJ peddaneni_h_Page_41thm.jpg
08403385a48837bef3f572f548f182aa
969c2bab08e6a286741003315d3d3912cdf7b183
15030 F20110114_AACIAR peddaneni_h_Page_07.pro
16e3f2087a43d23f1390af87ac8d7098
ab39420f7c2dcde500db13410c1305f1af63d5a9
F20110114_AACIKM peddaneni_h_Page_44.tif
573151718c7c228c3a8dd64ca3e09e30
8c09bdccc44cbe26ba4029787f4be87f16eedd1c
57284 F20110114_AACIFP peddaneni_h_Page_09.jpg
2927dbb2fd19f891191cd0327140f1ae
cbc2aa32bfda05f1fed9ab8fc4a2818cf7fa3527
3547 F20110114_AACIPK peddaneni_h_Page_42thm.jpg
639f4ff08336eba78abd9938fa23fc10
7c7fb9bbd24de0a1ff01d5b7a33c427ab929cee1
F20110114_AACIAS peddaneni_h_Page_26.tif
12a3fc4718adbda977d321c79dfa3136
244ed13f8baee630ee412abfce9c9a68d079463b
28118 F20110114_AACIFQ peddaneni_h_Page_25.pro
4ff8185b4ee546b132735fd7d0452e34
45dc59a9cf483cc8b67c8cc466129b879da25a2b
12710 F20110114_AACIPL peddaneni_h_Page_43.QC.jpg
769f2a51b6eda187de7c3b82cea2c7fe
bab23858a237ddbc570fee7d8ca7eba2c217456a
F20110114_AACIAT peddaneni_h_Page_31.tif
df9520b4395a46b4caba3a84d9c548d9
59cef520317bb2407cc45a2bb88f6dcfbc2a0ed7
F20110114_AACIKN peddaneni_h_Page_45.tif
37174758b19ac0c4a9a63b6d4a311fb5
b82c4329de7409cb511027ac7841929893ee2936
12475 F20110114_AACIFR peddaneni_h_Page_42.QC.jpg
be5f4bd8a89ad3feda51f7cc0241ebab
2f282ab3e9296b83ab68a589bd63d98312d0b0a9
3553 F20110114_AACIPM peddaneni_h_Page_43thm.jpg
87924c09e4ffe52448c03a7cd3b174c8
ceaf7ad3e39076e3db829e3294d32f30cb1c8420
57294 F20110114_AACIAU peddaneni_h_Page_26.jpg
7657081675e5660e4ef66b9dba02dae7
f1022458df63763c5ef635dfeb97c1246d1223a2
F20110114_AACIKO peddaneni_h_Page_47.tif
24cc090f621ab73a4783f180a68a34f0
2c703f7eb4e5f71385415b79557515e7fb7f18c3
23942 F20110114_AACIFS peddaneni_h_Page_44.QC.jpg
c1b4c1cda1538e0230161457310534f8
11bf619680b9bc417ab8fda3686ce85103439c3a
12498 F20110114_AACIPN peddaneni_h_Page_46.QC.jpg
6294094d3d02bb2be8bae25e5f273800
5117f2d7587b8bc94685fa8180046b3e585af1bb
61384 F20110114_AACIAV peddaneni_h_Page_34.jpg
e417c64189613973e68a725d2fa0c2b0
913bd5e18a88b5e7430b830c61aed9f46d91d820
F20110114_AACIKP peddaneni_h_Page_48.tif
cd4dffa3f1152825ea3003b2282b5aa4
ad0fd934f444a1cb5f82adcfeb75c426e173817b
3707 F20110114_AACIPO peddaneni_h_Page_47thm.jpg
5f9b2c6af8ba4108d08df9787ab0a468
c75313a3ed52c847b64a5f1d95bd7d14e646639f
4125 F20110114_AACIAW peddaneni_h_Page_31thm.jpg
dbcd31611d07d875a4cf09ab3ad3ecbe
d70115297d432c54c44ff79eb228281f16b9c901
F20110114_AACIKQ peddaneni_h_Page_51.tif
98e62e529f15a59811a4ebd956e4db7c
8fe8b2f68513e14134ab6ca6b1561e1dd45d0c18
1051945 F20110114_AACIFT peddaneni_h_Page_21.jp2
af7478bab4729ccfd0c8759bbcf4135d
80bc8f46f11c1fec16dbefc2e7ba6848881a60dd
13376 F20110114_AACIPP peddaneni_h_Page_48.QC.jpg
a43bcbaf1faef82c6d7c5a0fd6d70868
ae8e069ec1be69cc2f22b315aa7dfd050e8dd5cb
916 F20110114_AACIAX peddaneni_h_Page_37.txt
7e36a78606771f01dc1fa676480c7d4d
435dc51daae93b431e3ab9854339fb8b324c8fbc
F20110114_AACIKR peddaneni_h_Page_52.tif
04ad9f99157c52c7c2144d8f37272fd6
07650a956fa565357bf4ac0267be77ab1e05c320
1089 F20110114_AACIFU peddaneni_h_Page_54.txt
31d1e416d8eaad988e4e3f8ff0f881e0
c6808d9f5daa95da6cc898a45ac081547093d150
24683 F20110114_AACIPQ peddaneni_h_Page_49.QC.jpg
6d2cc693f1711efceb442090aa59a514
96d845e30276c1062430f968a67bb1cecab42650
1390 F20110114_AACIAY peddaneni_h_Page_32.txt
2b95ed0dd05808ca27a09767584d276f
99193cfd92da3e58625706dce808a7d38e146b98
F20110114_AACIKS peddaneni_h_Page_54.tif
4f4344adfaa36af2b5a84670aa07fb0b
85927bb60a601add4da1b39bbf082435b3c008c9
3587 F20110114_AACIFV peddaneni_h_Page_32thm.jpg
1ab37660dcf3c6c33735d73c70af1e3b
9d35c2e5dee93b6c244261e5784002e7635b66ab
6565 F20110114_AACIPR peddaneni_h_Page_49thm.jpg
7ac374a21dc4495cdc6fa8676b796ba4
00ce39e3d5b55701c180d814e967b71cebe6031b
63211 F20110114_AACIAZ peddaneni_h_Page_05.jpg
24855cdf66a18d6277f771f87b93b67c
9debf9ca23a1495bf322c4d6207dd577d53327b9
F20110114_AACIKT peddaneni_h_Page_55.tif
66514321aff5d66f8053af0b25cf2cb5
03690e44965e2919b2e4f0af4c82f3d4d053f66c
6145 F20110114_AACIFW peddaneni_h_Page_21thm.jpg
c57a7241e31c3ab91b6cbb68d64ac551
d409a05ed30b46dd011d558e5dcd29fc3db511de
F20110114_AACIKU peddaneni_h_Page_57.tif
81a6e4ae648e0aa0b34e5a4f526e1156
927d953d0fcd2373f87d9bb4504f0a483420a33b
59303 F20110114_AACIFX peddaneni_h_Page_52.jpg
23791b1a5f21bc950050a65855c2b5f3
50ef83ea4a2d82b5d40470839ada464935f59cad
23436 F20110114_AACIPS peddaneni_h_Page_50.QC.jpg
55ad3593cfacc2100b83831bfbd22da6
bb9d3ead599623a2ba0a9545236f148062dd0e7e
7041 F20110114_AACIKV peddaneni_h_Page_01.pro
fccfcbd78fcfb02d4ee0fbfebae88aac
d6962ce2931db68d9d089b9a123922b842bacd4d
F20110114_AACIDA peddaneni_h_Page_22.tif
ae369b2eb7f100b63e9c4013e0a3aab1
c7ceb9ccf8e86068012c19dd7cd076b4c6871c6a
39255 F20110114_AACIFY peddaneni_h_Page_26.pro
0d310802483fa42b7bc27dd68d5ae218
22ee3fb6f7ec0a5f32a8e34c15036a51797425aa
6595 F20110114_AACIPT peddaneni_h_Page_50thm.jpg
37c794328806ad3ee54805258ec3ac25
8e0fd784a17ac5741ed95d51b44159a14c8b3909
70243 F20110114_AACIKW peddaneni_h_Page_05.pro
c43c025e7518113665fe6e4d2091aabb
86c5c13a353bb3e7509bfcfae5451e6ff3146938
6662 F20110114_AACIDB peddaneni_h_Page_01.QC.jpg
9a4b1cbde45dd98c009140e8f336aa62
0273724fe932c4df3f8a4607699921759afbb30a
5260 F20110114_AACIFZ peddaneni_h_Page_25thm.jpg
9e242e98b1e78f89ab95e53ee4545dc4
ad40952edb65018dac728bfdd6ff01973d164d6c
19640 F20110114_AACIPU peddaneni_h_Page_52.QC.jpg
55b389be89296c3075afcd7938d4b5e7
ffebc65789a51b5b055b0b6232ebeae10107a165
61432 F20110114_AACIKX peddaneni_h_Page_08.pro
171893d4240174df25e0efe0eec66bcf
eb78179c43470c40bed6d0fc843a03dbc0d4fe38
590450 F20110114_AACIDC peddaneni_h_Page_37.jp2
f096a9b37522ba7367f2cb3b01b0ab05
debe2bc6917fdf1398fc9dc3d3c22cc7cbdef8cb
5479 F20110114_AACIPV peddaneni_h_Page_52thm.jpg
4fc3e5a8fe0000d1e5d38cf91723ab79
f6c5cb0528e4c0df18c22049f459d928721925ef
51800 F20110114_AACIIA peddaneni_h_Page_48.jpg
adbb5949c3bdfde4d624b5bf04799ae5
44cd2877bf1ebfee78b18fa4146323c193310260
35750 F20110114_AACIKY peddaneni_h_Page_09.pro
4f9a2004d5fab29d5dba8e0b48b523d2
3d82ddd647c229f279d70736eab0a1a6cac00873
6516 F20110114_AACIDD peddaneni_h_Page_44thm.jpg
633fc0e890bbadd85098cf9bdc4d693e
da38aaf851c09198236e7b161834f0fa3ae162cd
22664 F20110114_AACIPW peddaneni_h_Page_53.QC.jpg
2151770dd4a4757b2b649dffb0a8c4da
990acb7e388a667eb75f8b6506c53f7e322fb338
85542 F20110114_AACIIB peddaneni_h_Page_49.jpg
b29412451e5ba7e865666825680bc485
d5335a0a76859ee4e92a2429348416fb8491d96a
11830 F20110114_AACIKZ peddaneni_h_Page_10.pro
93b7e9e8906807aebab4890cd3506e43
f71101ce946606fcb21fb928dd2b19338c2286bb
2162 F20110114_AACIDE peddaneni_h_Page_55.txt
5ae95fe8a67b723603de9ad8c871cfb8
4dd9f3517029d9dee1384547f8a2cd260c4e1cf5
4281 F20110114_AACIPX peddaneni_h_Page_54thm.jpg
fee374c5b7f83833017426e880c042bc
92b2417cb49fc8dd5bc99869df5f15e40432c3d7
70278 F20110114_AACIIC peddaneni_h_Page_53.jpg
9602b33f3e20732e3f661355f0a24c2b
aee780ac2019c50aaec4b50aed665d2b5b31382e
46132 F20110114_AACIDF peddaneni_h_Page_40.jpg
41c165d43884fbf33e4005a62d90804f
02ba77b8be9026a5467d2be40fe592241e774fc8
22499 F20110114_AACIPY peddaneni_h_Page_55.QC.jpg
5aa60155e3a17a485d4683ed5610ee70
7a4816339556414ea58b018181a7136a97888603
75579 F20110114_AACIID peddaneni_h_Page_55.jpg
75a8381d215a27a81323766df35dcacb
dcdb83f26de7dec96592ef01e87e02af1875d980
1374 F20110114_AACINA peddaneni_h_Page_34.txt
95c5890918510f51fdc95a97e146b731
9f955fc0933552c93ba0a6b7769b28b60863160e
26511 F20110114_AACIPZ peddaneni_h_Page_56.QC.jpg
6781be41e4f56b74415808eba3590af6
db7f3e7d18a688dfb9a86570a31c9ef94f0f57e9
90315 F20110114_AACIIE peddaneni_h_Page_56.jpg
35e8d576385baecad9e6b0e3ffd0cf4a
cda2b569e6ac5c2076050250496e094cca01049a
4775 F20110114_AACIDG peddaneni_h_Page_45thm.jpg
771a97f029942bc16cfc846010af2cf2
62d4d4ddcb2174498a64fff6619f23300c3cb469
F20110114_AACINB peddaneni_h_Page_39.txt
f26227bf5c199bc9c293d0dec6f11358
6af5a934e69f87ab70326d885c289213cae36aea
21612 F20110114_AACIIF peddaneni_h_Page_01.jp2
731dce7582c490a690dae443a2541fc8
9be7c2e6f41ad5dacffdad88e985b357bc8fd2a6
12301 F20110114_AACIDH peddaneni_h_Page_57.jpg
9fcb33caa2860b97983cf853364c6004
4cc447ed794099210b99574521fe5e2b3fcb88d8
1385 F20110114_AACINC peddaneni_h_Page_40.txt
2b222e9d393e0b5329df3a0cbf329a92
b51d73031c81733a95c64f3e7441b44b51ea3e17
5806 F20110114_AACIIG peddaneni_h_Page_02.jp2
7438a3ef72d6c5a47ba3a56464dd33d7
4ed356d22999cb051d87cc0bbb746a25c7a1d006
40850 F20110114_AACIDI peddaneni_h_Page_35.pro
18f3f3c1eac70242ad5834df2d2c2d00
318bd0a0466e85f18553aecf5f3bf9698ec72feb
1479 F20110114_AACIND peddaneni_h_Page_41.txt
2ab3c5af6a8449a9c79bf5407a45e1b0
7f44537d2287a7d46a587f1c9b38b88d6aa78348
1051984 F20110114_AACIIH peddaneni_h_Page_05.jp2
2c08d83ff3b1e99580f7733567e383ae
4b2623c1f7c17ee87d2fedf723043c63a16aebd4
F20110114_AACIDJ peddaneni_h_Page_56.tif
5263042667a12670a1680283f6f6190a
e02c2e868fc8e810ebc4360ea902d24788c800ba
1320 F20110114_AACINE peddaneni_h_Page_42.txt
fa33e6836f76fe0a6b4ef3890bc16178
e2878df21508e26763eacd51f3379bee20916e9f
87024 F20110114_AACIII peddaneni_h_Page_06.jp2
39812b477bbd18bac2c18974e14a41fc
ffb93c849952d7a5cfde459c814a9fe8d191f83d
6645 F20110114_AACIDK peddaneni_h_Page_53thm.jpg
b82a37912c2b636fc6a8871691f1005c
c1a7948086f823164f4191b4e2769f20bbbe188b
1191 F20110114_AACINF peddaneni_h_Page_43.txt
efd6b5319ee0f4bbeaf134f21e122d12
bcb17421f8533c94699e5a0b3d4b27410b7a43c4
488519 F20110114_AACIIJ peddaneni_h_Page_07.jp2
9d831c29d354bb8bf3580a792b255207
71ae4fe7e26bb562d46bcbcfa88d42ca3702e69a
14707 F20110114_AACIDL peddaneni_h_Page_54.QC.jpg
481f2c421b541191a174569359fee216
6f30d5371aa15d4e5ffe49dd84057f5dbded06d8
1195 F20110114_AACING peddaneni_h_Page_45.txt
bf3491c6d707204178a1d83a88094bed
3c63922a052bf169ea624a9524544ba89a606c9a
678071 F20110114_AACIIK peddaneni_h_Page_12.jp2
7cc1c2678ae0e3a581844bc85aa7d02c
a4547a52bb1fb3ccadcec7e4f690c6c69f7d84ff
6224 F20110114_AACIDM peddaneni_h_Page_33thm.jpg
dbf875f2bb44edd7f7faa30d878c8342
6e83302f1c5f42b76bb90835fba869948538c764
1016 F20110114_AACINH peddaneni_h_Page_46.txt
86cc61c7e0dbd4db3579c142c6411d9f
532feaa0490fdc008d971185283491cdc0759eea
45723 F20110114_AACIDN peddaneni_h_Page_49.pro
8cebb64126fedbdfe5d8aebb9d49b686
e84d7237caa7e23bf7f7606f065ec64d69972c65
1337 F20110114_AACINI peddaneni_h_Page_47.txt
cba199e6db0e734213fb3b6c8121bd9e
90bcf6a2fd6cf626d36149eb5f64ccdc5e8b955b
112230 F20110114_AACIIL peddaneni_h_Page_15.jp2
f3fc824e5cc4a0b4bc6167cc81f3a6f2
ac09fae1d06b0af8685fd40084d78d8b3cd9075d
F20110114_AACIDO peddaneni_h_Page_42.tif
c87ff07907be38babb7abfd5e4e6480a
b2d14736911d022a2da75fe08071cab7ed7c0cbd
1377 F20110114_AACINJ peddaneni_h_Page_48.txt
d0e28309f30e7c4b631f547f4a3c9d01
3ae2fa1170a1a56df2ae72369115f1286dac23f1
107693 F20110114_AACIIM peddaneni_h_Page_16.jp2
44e094f117f75691caf4d7abc9fd44bc
63493a82d2535f469e20c8bc1e76f0740b4fff5f
6166 F20110114_AACIDP peddaneni_h_Page_27thm.jpg
bb59b4fdd25e3bacb52ba8eacf795df5
c1d82e09115fd91d6d47288dc88b61ceb92b9d01
2074 F20110114_AACINK peddaneni_h_Page_50.txt
8c1d2b7a7c4eb5af543ea903cb51aa25
07014019ae4a06a90cf513a4f1d4263dd1162db4
92086 F20110114_AACIIN peddaneni_h_Page_17.jp2
f12c9494fd7aa8bf5dca22d7c4c075f6
cd3d8e57312e5930b7b58b059bc18931faa24dec
F20110114_AACIDQ peddaneni_h_Page_09.tif
5d02ed1d9ec5c011060657aa0138a711
88d880eff7e0cecf1a445af7deb133ae314746f6
1223 F20110114_AACINL peddaneni_h_Page_51.txt
b271942be6a5ff65c3b22cf2e8254af2
a9d10e0ccd19a9e17df20a9bcc7517cd0d1ee5aa
86521 F20110114_AACIIO peddaneni_h_Page_19.jp2
b8ef4eb31b1648e06734d3471ec61a11
4e4b6512886470407aaaf0ad8c0a2079226a98c6
1718 F20110114_AACIDR peddaneni_h_Page_35.txt
d5167d59caf71499cf66c8d5917cd3bf
a9ec0c327a21abbe19c18c0846f9c39db6e4e1a0
2542 F20110114_AACINM peddaneni_h_Page_56.txt
b8de9416145c3a4d794a49c8f07560f0
3e07d0f10c7a19bd0db0fc4ba0e7eb3de402fa53
65245 F20110114_AACIDS peddaneni_h_Page_33.jpg
17d5d9d8639e2c019365f6d1bcb39a50
7cde4ad0c01b49f5c6c718dc7cb64555e5a9a202
169 F20110114_AACINN peddaneni_h_Page_57.txt
9170506c5f83fb9c8fdced115d1f36ea
3a681badc829714b20fa71156de8aa4eb3fcc718
82394 F20110114_AACIIP peddaneni_h_Page_20.jp2
061c697e4855285995abaf78f23ca650
160a790223b7dc49a16e02eb24d146501595ee0d
5837 F20110114_AACIDT peddaneni_h_Page_26thm.jpg
dc09dd31f138769715c7347c15a0cd86
f7347d58911b184c37d1b07f0950153402226999
679 F20110114_AACINO peddaneni_h_Page_58.txt
dbd103299019b3e87e523344918f8a51
2af74215fd6c9adf7955d966ebb4c8df183554ad
65085 F20110114_AACIIQ peddaneni_h_Page_23.jp2
c2c49deda2786fd1675652a305c689b6
6e76e261ab32dcb3325bca0f98a38f6390f65ed0
F20110114_AACIDU peddaneni_h_Page_18.tif
7d22f86f94fbbd68daf06888e548e7d3
eb0609a8f362ef5572769937999a253724eff57b
2252 F20110114_AACINP peddaneni_h_Page_01thm.jpg
4e9a6c1df9547b67451cbefc3d2a89d2
1726c535b1606b49b2060a2ff7812ef998322dda
88959 F20110114_AACIIR peddaneni_h_Page_24.jp2
90c4b77baae96e8fa0a037b871872d16
cdd0263621bc1a04686c54697da29eab9e2c06fa
1922 F20110114_AACIDV peddaneni_h_Page_53.txt
4ab6b068818b9dc014cc149f5c9d9033
353d8eea28792643f08a98a7c2f3b71313ad3db4
67913 F20110114_AACIIS peddaneni_h_Page_25.jp2
325ed34ecdfd2f2713b6ddd8285a0c19
ae79d6edf44dd84bf66dcf505c9cc071b0f0b4b8
3488 F20110114_AACIDW peddaneni_h_Page_06.QC.jpg
7c6cc3e7dfcda8af5d224526b664010e
a6a3bd63dcb9f5a5309bcef2a06a556b910d4829
1137601 F20110114_AACINQ peddaneni_h.pdf
9b9390e6637c132b6769b0a534f7cb07
20167973d1315266c67360698f68b9a0bf301a53
95147 F20110114_AACIIT peddaneni_h_Page_27.jp2
b8c8a0344b6987f5e9ca01ffeab35497
20e3c75269ccb74bf4cff942a4e07bf16f343cd4
26058 F20110114_AACIDX peddaneni_h_Page_04.pro
4e0c72166449e88b55beac4cc79cd8c8
11df5a375ba1452db6cd98c5401e53a5a38f99b8
90125 F20110114_AACINR UFE0007480_00001.xml
ed88dde9d123797439216486e9006277
ac83bcb7a6a7f20b2be4aa6e7777a61be2824cda
84713 F20110114_AACIIU peddaneni_h_Page_29.jp2
ec5e6c36cb543511e2b8292274532ee7
73e66882e8bb0fd559afd2399de547cf59023b0f
13639 F20110114_AACIBA peddaneni_h_Page_39.QC.jpg
38282839f95b222b250a2bc7d4f7c5f2
9c16ca804c7b67ce2f3a4abe1d53b40b12476146
F20110114_AACIDY peddaneni_h_Page_11.tif
dc09185dae283fb4678341f13a28fd30
1682d05921b74077b0b93ad72d18bb6719350740
3337 F20110114_AACINS peddaneni_h_Page_02.QC.jpg
3f0013cc3d545582e5a9e81d4cbd19a2
77ad3e0947036d33c03f4f23e2809a1d7683414a
84696 F20110114_AACIIV peddaneni_h_Page_30.jp2
b7ea5736ec9d3b941e443482bf3a5d9b
7dd47914605f896b6e86d50c67d5cbe5418ed36a
108244 F20110114_AACIBB peddaneni_h_Page_14.jp2
750ef1a54ebc0da5a6fe953092b2c919
4e9c36c272d830f9fde39283be0aa9e51f0ae989
42367 F20110114_AACIDZ peddaneni_h_Page_31.jpg
e8d1542f7fd8a7ddcaadd2334114ea5d
010daafeae8761d7168c9fd65c1b577fb412ba1d
1398 F20110114_AACINT peddaneni_h_Page_02thm.jpg
0cc0fee76bddbe86d3a87fab06beeb8d
3109460067da8be31078a55e14f99874c90da061
58387 F20110114_AACIIW peddaneni_h_Page_31.jp2
8b6813bdbed8308dfda64f1de27dce56
555e08d909a3894f2aee7444240c87eabeae19e6
1542 F20110114_AACIBC peddaneni_h_Page_57thm.jpg
753ba4c949f61aaf59df5fb5d4ea97f0
198d9206ea3ce812da9e6e7e839590c11c03bbe7
F20110114_AACINU peddaneni_h_Page_03thm.jpg
e3f20a96fb061c79dd92e7226aa7e77d
d9690b9fd207fe16e462e0a3d4572b03084046a5
46324 F20110114_AACIIX peddaneni_h_Page_32.jp2
41d0875bd9ddbfd3e74725aa93676815
1e0744eacb4022c5be0e3698efaf97a4107e6a74
14698 F20110114_AACINV peddaneni_h_Page_04.QC.jpg
c37189dabf630384de7b7d2f8d7c2179
330eed73b644f57a732589ecb7e36950ea87c54b
2127 F20110114_AACIGA peddaneni_h_Page_44.txt
b575653d343bd72ccef204f0e96ab5f7
5a10e72fe15432f551ca044b79466b28f4298d0f
95991 F20110114_AACIIY peddaneni_h_Page_33.jp2
c7871fe63f598401bdf44788c9b3dfe1
328a0001cd721fb935e946a01e6b48c02eb67dac
2954 F20110114_AACIBD peddaneni_h_Page_57.pro
c75ecd0fd050b998f913fc64650da3d1
4640eeab30ea6ed7b84788d70ce5fedc838e9301
4619 F20110114_AACINW peddaneni_h_Page_04thm.jpg
745e8dfe3a4d31df0007cbfcc89e1efa
1884a08e86bbaded80c27c5a3d6f1f02c3742865
F20110114_AACIGB peddaneni_h_Page_50.tif
5c125b7fd3b3f1268db933ea5e8b7e8e
788114e5ac1fed2edbcb9311b0e480b8cd452c7f
880539 F20110114_AACIIZ peddaneni_h_Page_34.jp2
21bf40cda087e7670fb3a88d9eb2469e
89a72304f486927a81521de7dd7a773ddc9bfe22
16481 F20110114_AACINX peddaneni_h_Page_05.QC.jpg
629219124503f7aa794c95248938027f
8db19137d0ece2a3e16c4d6af62b329d6936e28c
F20110114_AACIGC peddaneni_h_Page_49.tif
dea265f8fe772530437ad4b680b6037e
f6f9c6698b5cabf308e5869000e6ec980b898a9d
60318 F20110114_AACIBE peddaneni_h_Page_04.jp2
e12c2a107a7832071c379922c8a7d050
cab0e2c102decf99398a0d3fc3fc544af936611a
51766 F20110114_AACILA peddaneni_h_Page_15.pro
3648ae9ffad1848fe7d7f00c8e837285
c972b1f3326c7e475b5ffe679bf7f210a9eceafb
4470 F20110114_AACINY peddaneni_h_Page_05thm.jpg
7eb90215b00bedc42b420a3768145b7a
4862f8c945fe531443348b8bb9b966c81b77247a
F20110114_AACIGD peddaneni_h_Page_16.tif
674bebffb31e5f46bf6648c3f4b123cf
f9690e3d8a5ea0b92ec30eeacc35fdc39a1e465a
47244 F20110114_AACIBF peddaneni_h_Page_46.jpg
9437e5efabbadd8460f7262c0bf87ed4
164f8b74cdcd9ac368a6ee053a7f455af411320f
49716 F20110114_AACILB peddaneni_h_Page_16.pro
3754465b882f2ecc70fddb004693ce01
95dcd0b8415ecc17d23f66002bcf162a53a46312
7138 F20110114_AACINZ peddaneni_h_Page_07.QC.jpg
f6e97dfd340ebcb08c256c9b5b8e7f35
c9ad18b18dd7d128f56666ad78817f2daabb533a
5873 F20110114_AACIGE peddaneni_h_Page_34thm.jpg
95b2b640c08303933238983695ce82c0
7e100161e378342418a1aa6b2de5bd266f2a16fb
37276 F20110114_AACIBG peddaneni_h_Page_52.pro
528c4955f5a274d3cbba72d64468858e
711aff6e9c9d4cf088dd9a1b67ec82071025e68a
42086 F20110114_AACILC peddaneni_h_Page_17.pro
b4b03b49c6830f7812e2fbed5734c46f
e129e80048b7429a6e1ef792ffa1a38c4f61c8ac
9924 F20110114_AACIGF peddaneni_h_Page_57.jp2
b11e8a9613c76df5d9bfe84863b05696
9f607ca06a9fcdf2f2c2c955f10fa14ea5920dc7
94596 F20110114_AACIBH peddaneni_h_Page_11.jp2
5b474869e24d5e0998cd81e9e6547681
8d63c304e795524dcd8dfe0130e6f03cecf633c2
7195 F20110114_AACIQA peddaneni_h_Page_56thm.jpg
5d57c499e2b0c30e15ef9afc04e682a9
8f0a7100f64591d8d55d42dd1d2b4de841dc807e
2861 F20110114_AACILD peddaneni_h_Page_18.pro
1984904f0f6183365b883db45ebb2159
27a42db6d6515b4ac7b33f8eb9c6546a0ee4c00b
F20110114_AACIGG peddaneni_h_Page_46.tif
2c2c4903e65ed1b3f81d8b6a208854af
ba78f13472209b773c5a83dcce6dc0b61459ed82
45891 F20110114_AACIBI peddaneni_h_Page_51.jpg
183c866ccdc211cf64c0e342a40043c8
73bb0173bf78d672946a032d8ca5cf83e88fd96e
4103 F20110114_AACIQB peddaneni_h_Page_57.QC.jpg
deabe819801233310f285487dcf9005a
f27860ab0386d86a1b07b0856d3e22166fab1da5
39476 F20110114_AACILE peddaneni_h_Page_20.pro
cfd9dab21c2c7c7180a251ab7f82128f
71163bffc198ae02380073d026c32e995fa770b8
F20110114_AACIGH peddaneni_h_Page_24.tif
c31e7086d020cb6ec4ca0b335f865d15
b7a5bcdc9c26ad63680b99c9d05829675567b0cf
3926 F20110114_AACIBJ peddaneni_h_Page_18.QC.jpg
b6fa5f519fa62fd0ecb579821543d087
fab5fbf196aa8d5f7c61b9e3235edee453751114
3081 F20110114_AACIQC peddaneni_h_Page_58thm.jpg
f763e2eb02fa8a2f18d35145ce53b650
d15dfb7475e2c53d25cabd3f012ccc38305ea8a4
34317 F20110114_AACILF peddaneni_h_Page_21.pro
4e4e5943dbbdfabde025f7a4cb812048
70ed18e25c02950a2e4373117e6991760536a5ca
39183 F20110114_AACIGI peddaneni_h_Page_19.pro
34ecaac570b4ea1165330608348694af
e5d6c0dedc6ac44ffcc9875219332479aa9ec586
73040 F20110114_AACIBK peddaneni_h_Page_22.jp2
f0c0cda85023eca79c02a609cecdffdf
0fd265a1a3c9799b00f4511bdfe7db224aa90667
34397 F20110114_AACILG peddaneni_h_Page_22.pro
83ed553dcf74e3bb60a5a73df7b51c02
2c798c9736a96375fcf8560ace09053a82a02780
57568 F20110114_AACIBL peddaneni_h_Page_41.jpg
23e7e88ca942ae3253f37b066ca43e17
a576f24051ee6001e02b1c014625fb0efcf6e09e
39351 F20110114_AACILH peddaneni_h_Page_24.pro
7cf36dfec8ce89f13b8fae7e5c407331
45bf07a12df618f84270d61ee2d8767f5b6c867d
85790 F20110114_AACIGJ peddaneni_h_Page_52.jp2
14b978350045ab189599e9ef6b577d2c
e4d0f964f20b57d73ff69b0ba0af705f1e7fd2c5
1403 F20110114_AACIBM peddaneni_h_Page_06thm.jpg
dd8d2e0d149b81f2133082d5b8ff6ea7
7d162c0124a228ee03a09b7c35440e42148906e9
43739 F20110114_AACILI peddaneni_h_Page_27.pro
5f0c27fc94f6717750ef3d051e98444c
bdd90052032e7d1d030119c9f519b29eb84e191c
53778 F20110114_AACIGK peddaneni_h_Page_51.jp2
ce7dc4030b8bf255fb69c170b357320e
82253f75c6fe840a154aa14058a25dbf9bf06c36
2465 F20110114_AACIBN peddaneni_h_Page_08.txt
b5cdbf63b692dd2939c6f03d3da4d15f
c1bb064551ba9bdad1720963f11e83cfdbf921bf
36190 F20110114_AACILJ peddaneni_h_Page_28.pro
c4780a0de638e323b9812151fd6315a8
8c9ec7fbe77480af41798891be665354719d6eb1
11604 F20110114_AACIGL peddaneni_h_Page_06.jpg
9d3d8920efd2f0832ba3d71ef4843beb
46c448110583229ceea3340f2edf7c4fc399357f
25123 F20110114_AACIBO peddaneni_h_Page_15.QC.jpg
9772d367f2bca2427ec978e8ad2b284c
5bb57811e7443d30e6143ab1c69ca7b93f43f22e
38145 F20110114_AACILK peddaneni_h_Page_29.pro
c5304cd235c22457bf263ad88585d057
2cc874064ef40238162be9f20c45c68a73ad64d6
15816 F20110114_AACIGM peddaneni_h_Page_58.pro
350798910231a6c4f98a2abccf06bb6a
fbad282d960ac0ed9b2141832b2a3071a3e14ce4
2036 F20110114_AACIBP peddaneni_h_Page_49.txt
5050c2fac4ef4df4cd688bf5b11eefdb
11ae77d677a838945859b11eb9b3393447f095f7
37815 F20110114_AACILL peddaneni_h_Page_30.pro
a04bb6959c860473b23c94c3b825b467
5b2f1ce8c51eb0cd8bec33d6770d35e24e105dce
F20110114_AACIGN peddaneni_h_Page_32.tif
793fb32d45714906ab67c0f3f37b056a
c234b4291eb7e9a2983bc9b202eab8a9d769ef95
62279 F20110114_AACIBQ peddaneni_h_Page_19.jpg
a997bb27406c409041ed5ef45dacf588
edd95bfefe6c7fcad22b05abac9b3449ad91803a
1984 F20110114_AACIGO peddaneni_h_Page_38.txt
4b73921321a26f3a88f2e507a7ef7958
1b61a9db938a09bf6f28f47419e0811f03a99cdc
73295 F20110114_AACIBR peddaneni_h_Page_28.jp2
9c6a12c207cb9bff95b596928a3b85d9
db7e76aba9f106e2d129946d6cd6c60722936205
25479 F20110114_AACILM peddaneni_h_Page_31.pro
9c8de7540c7e22e7cc1cd18ac49e5802
645feacf47a3897781618050f23583bf9f11d6b8
6081 F20110114_AACIGP peddaneni_h_Page_17thm.jpg
464797659a3add2816144b30bfa50c21
514c5a93fe96a79d87c7b19e07ae9cfa1769c6da
5843 F20110114_AACIBS peddaneni_h_Page_08thm.jpg
80b3e036da2d91e6455a4a02b0edd232
5f78f2380d0363d103ecd693a26b72040a8b5a31
21466 F20110114_AACILN peddaneni_h_Page_32.pro
0972e6c4933c4a0c3fc14883030c9473
4baf7e8cc16f122107a939fc1ebfdaf5f7938c50
1599 F20110114_AACIGQ peddaneni_h_Page_29.txt
40c9fef3210b9202a07d317b2fe2382e
65898d16a0d64b6848f074334b5e9f15df7e2356
29930 F20110114_AACIBT peddaneni_h_Page_58.jpg
d69f7a2464c95b1554eefd0ac7c10dfd
913c5ef5747793d69e44b80cf5f082095889ef7f
20825 F20110114_AACIGR peddaneni_h_Page_19.QC.jpg
d5eac2acc63636fdc4565e66ae614ea4
db008b3fc52e1555ba8fa42f1c7d67fd0503516d
F20110114_AACIBU peddaneni_h_Page_39.tif
fc549ef9b77be0572ca1b44923550533
4db9ffe599d9660155440ca81ede2402d87335a8
45004 F20110114_AACILO peddaneni_h_Page_33.pro
52ecffdd347b1a244e7e00ae5230c98a
e5ec821d88aad3e19ac545503b105ff372c62593
F20110114_AACIGS peddaneni_h_Page_28.tif
8f6042f360d90cf1601c2e8ce6e4d882
05a7108102318014b7106c7382546c244621cd59
2030 F20110114_AACIBV peddaneni_h_Page_15.txt
8709272a72e97308b06feb5d3a3bc334
63a8e11d61ce19fae2944b0c9e0fcc37aaff9ece
31599 F20110114_AACILP peddaneni_h_Page_34.pro
7256381852ef5e2d1d37ed27fd127617
754134adf1401b7d33b7d8cac2c657c0d047db36



PAGE 1

COMPARISON OF ALGORITHMS FOR FETAL ECG EXTRACTION By HEMANTH PEDDANENI A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2004

PAGE 2

Copyright 2004 by Hemanth Peddaneni

PAGE 4

ACKNOWLEDGMENTS Any accomplishment is possible only when there is a motivation and a guiding force. I am highly grateful to my advisor, Dr. Jose Principe, for providing both of these. His suggestions and encouragement have been of immense help for me in completing this thesis. I would like to express my gratitude to Dr. Deniz Erdogmus and Dr. Yadunandana Rao for the many discussions we had, without which the work would not have been completed. I would like to thank Ms. Dorothee Marossero for providing me the ECG data sets and for her help in evaluating the performance of the algorithms. I would like to thank Dr. Michael Nechyba and Dr. Fred Taylor for serving on my committee. I am thankful to my friends at CNEL, Anant, Jianwu and Can, for providing a friendly atmosphere and lending their hand whenever I had some problems. Finally I would like to thank my family members for their support and love, which have been of utmost importance for me to complete the present work. iv

PAGE 5

TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES.........................................................................................................viii ABSTRACT.......................................................................................................................ix CHAPTER 1 INTRODUCTION........................................................................................................1 Problem Description................................................................................................1 Past Research...........................................................................................................3 Goals of the Thesis...................................................................................................7 2 DESCRIPTION OF ALGORITHMS STUDIED.........................................................9 BSS Using MeRMaId Algorithm.............................................................................9 BSS Using Minimization of CS QMI..................................................................14 BSS Using Generalized Eigenvalue Decomposition.............................................17 3 RESULTS...................................................................................................................23 Data Collection......................................................................................................24 Performance of the Algorithms on Normal ECG Data..........................................25 MeRMaId Algorithm...........................................................................................25 Cauchy Schwartz based Quadratic Mutual Information.....................................28 Generalized Eigenvalue Decomposition Algorithm............................................31 Performance of the Algorithms on the Data during Contractions.........................34 Comparison of the Performance of the Algorithms...............................................39 4 CONCLUSIONS AND FUTURE WORK.................................................................42 Conclusions............................................................................................................42 Scope for Future Work...........................................................................................43 LIST OF REFERENCES...................................................................................................45 v

PAGE 6

BIOGRAPHICAL SKETCH.............................................................................................48 vi

PAGE 7

LIST OF TABLES Table page 2-1. Summary of procedures for BSS using Generalized Eigenvalue Decomposition (GED) for fetal ECG extraction................................................................................21 3-1. Comparison of performance of the BSS algorithms for normal ECG.......................41 3-2. Comparison of performance of the BSS algorithms for ECG data during contractions...............................................................................................................41 vii

PAGE 8

LIST OF FIGURES Figure page 3-1: Position of the electrodes on the pregnant woman...................................................24 3-2: Eight channels of normal ECG data. Only 2000 samples of the ECG data are shown in the figure....................................................................................................27 3-3: Output signals for the MeRMaId algorithm. The nature of the eight signals is mentioned to the left.................................................................................................28 3-4: Plot of the signal to interference ratio versus the iterations.....................................29 3-5: Learning curve..........................................................................................................30 3-6: Output signals for CSbased QMI Minimization....................................................31 3-7: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition method using non-stationary assumption..................................................................32 3-8: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition method using non-white assumption........................................................................33 3-9: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition method using non-gaussian assumption....................................................................34 3-10: One channel of ECG data during uterine contractions. The figure shown at the bottom zooms on the portion of the signal containing contractions.........................35 3-11: Output signals for the MeRMaId algorithm............................................................36 3-12: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition method using non-stationary assumption..................................................................37 3-13: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition method using non-white assumption........................................................................38 3-14:2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition method using non-gaussian assumption....................................................................39 viii

PAGE 9

Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science COMPARISON OF ALGORITHMS FOR FETAL ECG EXTRACTION By Hemanth Peddaneni December 2004 Chair: Jose Principe Major Department: Electrical and Computer Engineering The thesis addresses the extraction of the fetal ECG signal from the non-invasive ECG measurements of a pregnant woman. This is an ideal situation for independent component analysis because the assumption that the two sources in the measurements, fetal ECG and mother ECG, are independent is verified at the short time scale used for separation. Three algorithms, Blind Source Separation using Minimum Renyis Mutual Information, using Generalized Eigenvalue Decomposition and using Cauchy Schwartz Quadratic Mutual Information Minimization, have been used to get the fetal ECG under normal conditions and during the uterine contractions of the mother. Minimum Renyis Mutual Information method uses whitening of the data and as such it is less suitable to extract the fetal ECG during contractions. The Generalized Eigenvalue Decomposition method turned out to give superior quality of the fetal ECG during the contractions. The third method, Cauchy Schwartz Quadratic Mutual Information Minimization, gave ix

PAGE 10

promising results for lower dimensional normal ECG data but failed to work for the higher dimensional ECG data during contractions. The quality of the extracted fetal ECG is compared using a criterion called Trust Factor (which varies from 0 to 1, 1 corresponds to the best quality). These results help in determining which algorithm is best suited for finding the fetal heart rate since the QRS complex is preserved in all three algorithms. x

PAGE 11

CHAPTER 1 INTRODUCTION Fetal electrocardiogram (fetal ECG) extraction is an interesting as well as a difficult problem in signal processing. This forms one important application of Independent Component Analysis (ICA) or Blind Source Separation (BSS), where one wants to separate mixtures of sources with very little prior information. In this chapter we will first describe the problem description followed by the past research that has been done in this area and then finally about the goal of this thesis. Problem Description Fetal electrocardiogram monitoring is a technique for obtaining important information about the condition of the fetus during pregnancy, by measuring the electrical signals generated by the fetal heart as measured from multi-channel electrodes placed on the mothers body surface. This method of recording the fetal ECG from the mothers body, without direct contact with the fetus (which is highly desirable) is called non-invasive method. However, in this method of recording, the fetal ECG signals have a very low power relative to that of the maternal ECG. In addition, there will be several sources of interference, which include intrinsic noise from a recorder, noise from electrode-skin contact, baseline drift (DC shift), 50/60 Hz noise etc. The situation is far worse during the uterine contractions of the mother. During these contractions, the ECG recordings will be corrupted by other electrophysiological signals called uterine electromyogram (EMG) or electrohysterogram (EHG), which are due to the uterine muscle rather than due to the heart. The response of the fetal heart to the uterine 1

PAGE 12

2 contractions is an important indicator of the fetal health. As such a need arises to effectively monitoring the fetal ECG during the uterine contractions. But monitoring the fetal ECG during these contractions is a difficult task because of very poor SNR. The nature of these contractions is shown in figure 3-7 of chapter 3. 0 20 40 60 80 100 120 -2000 -1000 0 1000 2000 3000 4000 P Q S R T Figure 1-1: Components of the ECG waveform The nature of the fetal ECG is similar to that of mother ECG signal and is shown in figure 1-1. The ECG waveform is also called PQRST wave. The first waveform in the ECG-the P waveis due to the atrial contraction. The next waveform-QRS complex-is due to the ventricular contraction. The final waveform is the T wave which occurs as the heart prepares for the next heartbeat. The location of P, Q, R, S and T components are indicated in the figure 1-1. The three main characteristics that need to be obtained from the fetal ECG extraction for useful diagnosis include

PAGE 13

3 Fetal heart rate Amplitude of the different waves Duration of the waves. But because of the non-invasive nature of measurement of the fetal ECG, most of the signal processing algorithms detect only the R waves and the P and T waves will usually remain hidden. Also fetal ECG extraction problem is not easily solved by conventional filtering techniques. Linear filtering in the Fourier domain fails since the spectral content of all the three components, maternal ECG, fetal ECG and noise are rather similar and overlap. Past Research The problem of fetal ECG extraction was tackled more than 30 years ago by means of now conventional adaptive noise canceling techniques. Widrow and Stearns [1] used a linear adaptive filter framework to cancel the mother ECG and obtain the fetal ECG. They used two sets of electrodes, one set placed on the abdomen of the mother and the other placed on the chest of the mother. The electrodes placed on the abdomen pick up both the fetal ECG and mother ECG (serve as primary inputs), whereas the electrodes placed on the chest pick up only the mother ECG (serve as reference inputs). So by having the signals from the electrodes placed on the abdomen as desired and the signals from the electrodes placed on the limbs as input to the adaptive filter, the error signal can be made to represent the extracted fetal ECG. This method although providing a solution, is not robust enough to be used for clinical practice. First one needs to have more electrodes to measure the signals. Second, if the amplitude of the background noise is greater than the fetal heartbeat, as is the case generally during the uterine contractions,

PAGE 14

4 the resulting error signal will not contain the fetal ECG. This method fails to extract the fetal ECG when both the mother and fetal ECG overlap. Further more, if there is leakage of the fetal ECG into the recordings of the reference input (mother ECG), the quality of the extracted fetal ECG will be extremely poor. The positioning of the abdominal electrodes is extremely critical to get a good fetal ECG. They will have to be placed at places on the mother where maximum amount of fetal ECG is picked up (again this leads to the issue of where to place the electrodes). Also in this framework, only second order statistics are used and higher order statistics are ignored. Camps et al. [2] also used an adaptive noise canceling technique to extract the fetal ECG but with the linear adaptive filter replaced with a time delay neural network (TDNN). This TDNN is nothing but an artificial neural network (like a multilayered perceptron) with the synaptic weights replaced by FIR filters. This is done to provide highly non-linear dynamic capabilities to the fetal ECG recovery model. They trained the network using temporal backpropagation. Again this method suffers from the same difficulties mentioned earlier. In addition training this neural network is not easy and is extremely computationally expensive. Care should be taken to decide on proper initialization of the weights, number of hidden neurons, taps per neuron in a layer and learning rate. Mochimaru and Fujimoto [3] used wavelet based methods to detect the fetal ECG. They used multiresolution analysis (MRA) to remove the large baseline fluctuations in the signal as well as to remove the noise. MRA was performed on the raw ECG data up to the 12 th level using Daubechies20 wavelets. The 12 th order approximation function consists of slow variations of the signal. This was subtracted from the original raw signal

PAGE 15

5 to get a signal free from baseline fluctuations. To remove the noise, they applied wavelet transform based denoising of the detrended data by multiresolution analysis up to the 12 th level using Coiflet24 wavelets. Noise removal was accomplished by thresholding the wavelet coefficients at each level. Weighted standard deviation of the wavelet coefficients at each resolution level were used as the thresholds at each resolution level. The fetal ECG was monitored by calculating the Lipschitz exponent [4]. The main problem with this method is its inability to locate the fetal ECG if it is obscured by the mother ECG. Since this happens two or three times in a 10 seconds period, it can be a major drawback. Also there is a need to set the thresholds on the wavelet coefficients dynamically during denoising, since the noise content is more during the uterine contractions. Again the performance of this type of denoising during the contractions may not be optimum since thresholding of the wavelet coefficients may result in removing the fetal ECG component altogether in the original signal. Vigneron et al. [5] applied blind source separation methods for fetal ECG extraction by (i) exploiting the non-stationarity of fetal ECG and (ii) implementing post denoising using wavelets. The blind source separation algorithm proposed by Pham and Cardoso [6] was made use here. This algorithm minimizes the Gaussian mutual information, defined as the ordinary mutual information with respect to some Gaussian random vectors with the same covariances structure as the random vector of interest, to get the independent components in the signal. Then the wavelet transform was used to remove the baseline drift in the extracted noisy fetal ECG signal. After that, the PQRST of the fetal ECG is amplified by using a non-linear filtering technique. After PQRST amplification, a wavelet denoising is applied to the fetal ECG signal with the following

PAGE 16

6 parameters: biorthogonal wavelet type, level 6 decomposition and the data adaptive threshold selection rule SureShrink of MATLAB wavelet toolbox. The problem with this method is that there are too many post processing stages, as such lot of parameters ( like choice of non-linear filters, wavelet for baseline removal as well as denoising, level of decomposition etc.) need to be determined empirically. Work has also been done to extract the fetal ECG using genetic algorithms [7]. The genetic algorithm approach for fetal ECG extraction, proposed by Horner et al. [8], is based on subtracting a pure maternal ECG from an abdominal signal containing fetal and maternal ECG signals. Subtraction via a Genetic Algorithm is supposed to be near optimal rather than a straight subtraction. The issue with this method is the need to get the maternal ECG signals whose shape is similar to the maternal ECG present in the abdominal recordings (which contain fetal ECG). So it needs to be determined exactly, where the electrodes need to be placed to pick up the maternal ECG alone. Kam and Cohen [9] proposed two architectures for the detection of fetal ECG. The first is a combination of an IIR adaptive filter and Genetic Algorithm, where the Genetic Algorithm is recruited whenever the adaptive filter is suspected of reaching local minima. The second is an independent Genetic Algorithm (GA) search without the adaptive filter. The main disadvantage of an IIR filter is that the error surface is not quadratic but a multi modal surface. So the presence of the genetic algorithm forces the algorithm to overcome the local minima and reach the global solution. The quality of the extracted fetal ECG using this IIR-GA adaptive filter is superior to that obtained using the GA alone. This method of combining an adaptive filter with a genetic algorithm is interesting and it

PAGE 17

7 would be nice to see how it performs when there are uterine contractions in the ECG data. Barros and Cichocki [10] proposed a semi-blind source separation algorithm to solve the fetal ECG extraction problem. This algorithm requires a priori information about the autocorrelation function of the primary sources, to extract the desired signal (fetal ECG). They do not assume the sources to be statistically independent but they assume that the sources have a temporal structure and have different autocorrelation functions. The main problem with this method is that if there is fetal heart rate variability, as is the case when the fetus is not healthy, the a priori estimate of the autocorrelation function of the fetal ECG may not be appropriate. Goals of the Thesis The following are the goals of the thesis: Assess the performance of BSS algorithms that use whitening of data as a preprocessing step. Use Cauchy-Schwartz based Quadratic Mutual Information minimization to extract the fetal ECG. Under varying assumptions on the data, use Generalized Eigenvalue Decomposition to solve the blind source separation problem. Compare the performance of BSS algorithms which include whitening and which do not include whitening. The rest of the thesis is organized as follows. Chapter 2 provides a detailed description about the algorithms which were studied to solve the fetal ECG extraction problem. Chapter 3 describes the results obtained using the algorithms presented in Chapter 2. Finally Chapter 4 concludes the thesis by making observations on the results

PAGE 18

8 described in Chapter 3, along with some suggestions for future research in this particular area.

PAGE 19

CHAPTER 2 DESCRIPTION OF ALGORITHMS STUDIED The extraction of the fetal ECG signal from the ECG recording of a pregnant mother has been carried out using three different algorithms. The MeRMaId (Minimum Renyis Mutual Information) algorithm for Blind Source Separation (BSS) proposed by Hild et al. [11], whitens the input data spatially before minimizing the Renyis Mutual Information between the outputs. The algorithm proposed by Xu et al. [12] performs BSS by minimizing the Cauchy-Schwartz quadratic mutual information (CS QMI) of the outputs. The BSS via Generalized Eigenvalue Decomposition proposed by Parra and Sajda [13] provides an elegant way of finding the demixing matrix using generalized eigendecomposition of the covariance matrix and an additional symmetric matrix (which depends on the type of assumption made).These three algorithms along with some of the practical aspects in implementing them for the fetal ECG extraction are described in detail in this chapter. BSS Using MeRMaId Algorithm (n) x ~ y (n) x (n) s (n) Rotation Matrix R Whitening Matrix W Mixing Matrix A Figure 2-1: Block Diagram for two sources/observations The above figure depicts the overall block diagram of the MeRMaId algorithm. The source signals represented by s (n) are assumed to be independent. These signals are mixed by an unknown mixing matrix A to get the observable signals x (n). This 9

PAGE 20

10 observable data is first decorrelated spatially by applying a whitening transform (more will be described about this later in the chapter). Once whitening has been done, the problem of finding the independent components reduces to a simple rotation. So we need to find a rotation matrix which minimizes the Renyis Quadratic Mutual Information. Let us provide some mathematical aspects of the whitening technique. The observable data x (n) can be written as x (n) = As (n). Let (n) represent the whitened data and dropping the index of time n for the sake of convenience, then x~ I]xxE[WxxT~~ ~ (2-1) (2-1) turns out to be TxxxT2/12/1RRRIWWRx (2-2) Comparing, the RHS and LHS of (2-2), we get, 2/1xRW (2-3) Representing, the covariance matrix in terms of its eigenvalues and eigenvectors, the whitening transform is given by TVVDW2/1 (2-4) where V is eigenvector matrix of R x and D is the diagonal eigenvalue matrix of R x Why should we do whitening? To answer this question, let us have a look at the plot shown in figure 2-2. The figure deals with two dimensional data (for the sake of visualization). We see that by rotating the whitened data, we can achieve the desired solution of finding the independent components. So after whitening, the optimization problem of minimizing the Renyis Mutual information is constrained to a rotation matrix.

PAGE 21

11 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 Source Data 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 Mixed Data -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 0 1 2 3 4 Whitened Data Figure 2-2: Effects of Whitening The whitening operation transforms the mixing matrix A to a new one which is orthogonal. As such, instead of estimating n 2 (assuming A to be a n n matrix) parameters in the mixing matrix, it is sufficient if we can estimate n(n-1)/2 parameters in the new orthogonal mixing matrix( since the number of degrees of freedom in a mixing matrix is n(n-1)/2). So in larger dimensions, we need to estimate approximately half the number of parameters of an arbitrary matrix. Another advantage of whitening is it normalizes the data automatically. So we do not have to worry, even if we use scale dependent estimators for estimating mutual information. Whats bad with whitening? The whitened data will be proportional to the power of the input data. If the observable data is noisy (like what we have in the ECG of a mother during uterine contractions), whitening degrades the already poor SNR by

PAGE 22

12 enhancing the noise component. So it is advisable to make use of algorithms which do not involve whitening of the data in such situations. The other two algorithms described in this chapter does not use whitening for preprocessing the data. Let us now go into details about minimizing the Renyis mutual information. Renyis mutual information of order [14] is defined as dyyfyfyIndddYYR11)()(log11)( (2-5) This equation can be approximated as nddddYYRdyyfdyyfyI1)()(log11)( (2-6) Both (2-5) and (2-6) are nonnegative and evaluate to zero if and only if all the outputs are statistically independent i.e. when the joint pdf is equal to the product of marginal pdfs. As such both (2-5) and (2-6) have the same global minima and hence (2-6) is a good approximation of (2-5), for use as a cost function in adaptation. Now (2-6) can be written as ndRdRndYdddYRyHyHdyyfdyyfyI11)()()(log11)(log11)( (2-7) So the Renyis Mutual information of order turns out to be approximately the sum of Renyis marginal entropies minus Renyis Joint entropy of the output y. Since xRy ~ the pdfs of y and x ~ are related as:

PAGE 23

13 RxfyfXY)()(~ (2-8) So the Renyis Joint entropy of y becomes: RxHRdxxfdxRRxfyHRXXRlog)(1log11)(log11)(log11)(1~~ (2-9) The Renyis mutual information can now be expressed as: RxHyHyIndRdRRlog)()()(1 (2-10) Since R is purely a rotation matrix, determinant of R is one. So Rlog vanishes. Also, we have to minimize this mutual information with respect to the rotation matrix R. As the joint entropy of , does not depend on R, it drops out of the cost function. The final cost function is just the sum of the marginal entropies of the output y, i.e. x~ )(xHR nddRyHJ1)( (2-11) The advantage with this algorithm is that you do not have to estimate the joint entropy at all, which is comparatively difficult than estimating the marginal entropies. The marginal entropies can be estimated easily using the Parzen windowing with a Gaussian kernel. The estimate of Renyis quadratic (=2) marginal entropy simplifies to [15] NjNkdddRkyjyGNyH11222)2),()((1log)( (2-12)

PAGE 24

14 where G(x,2 2 ) is a Gaussian PDF and y d (j) is the j th sample of output y d The argument of the log in (2-12) is called the information potential. BSS Using Minimization of CS QMI In order to compare the performance of the algorithms which does pre-whitening of the data before minimizing the Renyis Quadratic mutual information, the BSS problem is solved using the Cauchy-Schwartz Quadratic Mutual Information [16]. The mutual information between two (or more) random variables can be measured using the Kullback-Leibler divergence: dxxgxfxfgfK))(/)(log()(),( (2-13) where f(x) and g(x) are any two pdfs. The corresponding Renyis measure of divergence between the two pdfs is given by the following equation: )1)(/)((log(),(1dxxgxfgfR (2-14) It can be seen that, we can integrate neither (2-13) nor (2-14) with the Parzen windowing method to produce a simple result. But if we use the Cauchy-Schwartz inequality to approximate the mutual information, we get the following measure: 222))()(())()()((log(),(dxxgxfdxxgdxxfgfC (2-15) We can easily see that, C (f,g)0 and the equality sign holds good if and only if f(x)=g(x). Let us now replace f(x) by the joint pdf of two random variables Y 1 and Y 2 and g(x) by the product of their marginal pdfs. Now (2-15) becomes, 2212211212121222211212212121))()(),(())()()(),((log),(dydyyfyfyyfdydyyfyfdydyyyfYYCYYYYYYYY (2-16)

PAGE 25

15 Now C (Y 1 ,Y 2 ) 0 and the equality sign hold good if and only if the joint pdf of Y is equal to the product of its marginal pdfs. We will now see how we can integrate this with the Parzen window method of estimating the pdf. The joint pdf estimate of the two-dimensional random variable Y={Y 1 ,Y 2 } using the Parzen window method is given as: NiYYIiyzGIiyzGNzzf12222112121)),(()),((1),( (2-17) The marginal pdfs can be estimated as: NiddddYIiyzGNzf12)),((1)( d=1,2 (2-18) We will make use of the fact that if ),(1 iazG and ),(2 jaz Gare two Gaussian functions with means a i and a j covariance matrices 1 and 2 respectively then, ))(,(),(),(2121jijiaaGazGazG (2-19) Let us now compute the terms in the numerator and denominator of (2-16) separately, NiNjYYIjyiyGIjyiyGNdydyyyf1122221122122121)2),()(()2),()((1),( (2-20) NiNjdddddYIjyiyGNdyyf11222)2),()((1)( d=1,2 (2-21) NindNjddYYYYIjyiyGNdydyyfyfyyf111232122112121)2),()((1)()(),( (2-22)

PAGE 26

16 where n is the number of dimensions in the data (here n=2). It can be easily seen that, the equations (2-20) through (2-22) can be easily computed and the cost function given by (2-16) can be evaluated. Thus, Parzen windowing can be easily integrated with the Cauchy-Schwartz based Quadratic Mutual Information estimation. Once the cost function (2-16) is evaluated, we can minimize it using any of the optimization techniques. The Gradient Descent has been used in the present work. In this the weights are initialized and they are adjusted iteratively such that the gradient of the cost goes to zero. The weight update can be carried out as: (2-23) nnnnaMDWW**1 Where =step size D n = derivative of the cost function at time instant n with respect to the weight matrix a=momentum learning constant M n = (W n+1 W n ) The momentum learning has been incorporated into this optimization method in order to overcome the local minima to some extent. As the iterations proceed, the weight matrix converges to, hopefully, the demixing matrix 1 The parameter which needs to be carefully chosen is the size of the Gaussian kernel, which we are using to estimate the integrals. By choosing any arbitrary kernel and doing the above optimization method, will not give optimal results. The method will invariably get stuck in some local minima present in the cost function. In order to avoid 1 Up to the order of scale and sign

PAGE 27

17 this, a concept called the kernel annealing has been used. Ideally, we would like our kernel to depend on the data as well as on the number of samples in the data. This makes sense because the same kernel size may be good for one type of data and may not be good for other types of data. Also if you have more number of samples, we can use a kernel with smaller variance and vice versa. These two ways of choosing the kernel size have been incorporated in the following way. 1. Choose the kernel size as the average of the standard deviations of the data in each dimension. 2. Scale this kernel size down by the square root of the number of samples of data. Coming to the kernel annealing part, we will start with a large kernel size. Then all the data samples are just like one sample compared to the kernel size. So the estimated pdf will be just like one Gaussian and the landscape of the cost function will be very smooth. Then as we gradually reduce the kernel size (in this case linearly), the landscape of the cost function becomes rough with multiple peaks and valleys. For half the number of iterations, we will decrease the kernel size and for the other half of the iterations we will search for the solution with the minimum kernel size (fixed) we have chosen. As a result of this the algorithm may escape the local minima and converge to the global minima. BSS Using Generalized Eigenvalue Decomposition Let s(t) represent n-dimensional sources, on which we impose certain assumptions (more on these assumptions later). Let x(t) represent the observable signals. If A is the mixing matrix, which is unknown, then )()(tAtsx

PAGE 28

18 The mixing matrix explains the various cross statistics of the observations x(t) as an expansion of the corresponding diagonal cross statistics of the sources s(t). Let R s and R x denote the covariance matrices of s (t) and x (t). Then, HsHxAAttERxxR)]()([ 2 (2-24) If the sources are assumed to uncorrelated, then the source covariance matrix R s is diagonal. Let us also assume, in addition to the covariance matrix, there exists other cross statistics matrix represented by Q s that has the same diagonalization property i.e. HsxAAQQ (2-25) It is also assumed that Q s has non-zero diagonal values, which ensures the existence of Q s -1 Let W be the demixing matrix, which we want to determine, such thatW. Now multiplying both sides of (2-24) by W, we get, IAH sxAWRR (2-26) Multiplying (2-25) by W and then by Q s -1 we obtain AWsx1QQ (2-27) Substituting (2-27) in (2-26), ssxxWWRQQR1 (2-28) Since both Q s -1 and R s are diagonal, their product is also diagonal. LettingQ, where is also diagonal, Rss1 QRWWxx (2-29) 2 We are assuming that x(t) and s(t) are complex valued variables. For real valued variables, Hermetian( H ) turns out to be the same as Transpose() T

PAGE 29

19 (2-29) represents a generalized eigenvalue equation, where W and represent the generalized eigenvector matrix and generalized eigenvalue matrix for the matrix pencil, R x and Q x So the demixing matrix is determined by the generalized eigenvector matrix of R x and Q x Let us now come to the different assumptions we can impose on the sources and the corresponding cross statistics matrix Q x In addition to the independence assumption, there are basically three types of assumptions you can have on s (t). They are: Non-Stationary Sources. Non-White Sources. Non-Gaussian Sources. When the sources are non-stationary, the covariance of the observations varies with time t i.e. HsHxAtAttEt)()]()([)(RxxR (2-30) (2-30) is in the form similar to (2-25). So we can set Q x =R x (t), for any time t. This Q x will give the diagonal cross-statistics of (2-25), required for the generalized eigenvalue equation (2-29). So the demixing matrix, can be identified by simultaneously diagonalizing multiple covariance matrices (here R x and Q x ) estimated over different stationary times. When the sources are non-white, we can use second order statistics in the form of cross-correlations for different time lags The covariance matrix for lag is given by: HsHxAAttE)()]()([)(RxxR (2-31) Again, (2-31) is of the form given by (2-25). So for any choice of the required cross

PAGE 30

20 statistics matrix Q x =R x (). This method of separating the mixtures of independent signals using time delayed correlations is first studied by Molgedey and Schuster in [17]. The non-Gaussian assumption of the sources is useful when the sources are both stationary and white. For such sources different t and do not provide new information and we have to consider higher order statistics. The 4 th order cumulants of the observable data x (t) expressed in terms of the fourth order moments can be written as: ][][][][][][][),,,(***********kjljljkilkjilkjilkjixxExxExxExxExxExxExxxxExxxxCum (2-32) When the distribution of x is Gaussian, the fourth order cumulant shown above goes to zero. If the distribution is non-Gaussian, the cumulant goes to zero only when the distribution of x is composed of independent variables. In [18] a linear combination of the fourth order cumulants is defined as: lklklkjiijmxxxxCumMq,**),,,()( (2-33) Noting that the covariance of x is and M= { m ][HxxExR lk }, (2-33) becomes, xxHTTxxHHxEETraceEMRRxxMxxMRRMxxxxMQ][][)(][)(* (2-34) Replacing M by I, makes Q x sum over all the cumulants given by, xxHTxxHHxEETraceERRxxxxRRxxxxIQ][][)(][)(* (2-35) Observing that x(t)=As(t), we see that HHsxAAAAQIQ)()( (2-36) where Q s (A H A) is always diagonal for any A. So Q x satisfies the conditions given by (2-25).

PAGE 31

21 Let us now see how each of these three assumptions can be applied to the fetal ECG extraction problem. For the non-stationary assumption, the cross-statistics matrix Q x is computed by considering a window of data of length equal to the period of the maternal ECG. The covariance matrix is computed using all the data. For the non-white assumption, the parameter is chosen empirically so that Q x can be computed to give the best performance. For the non-Gaussian assumption, there will be no parameters to choose and Q x is computed as the sum over all the 4 th order cumulants. Table 2-1 shows all the details of the blind source separation using the Generalized eigenvalue decomposition method. The observable data is represented as a matrix X of size NT, where N is the number of sensors (channels) and T is the number of samples in each channel. In MATLAB, the demixing matrix (W) is calculated as shown below for all the three assumptions: ),(],[xxeigQRDW

PAGE 32

Table 2-1. Summary of procedures for BSS using Generalized Eigenvalue Decomposition (GED) for fetal ECG extraction Matrices on which GED has to be carried out Sources are assumed to be R x Q x Details Non Stationary and decorrelated XX T )()([ttEHxxt:1(:,):1(:,X = Tt)X t is the number of samples over which the signal is assumed to be stationary(chosen to be 120) Non-White and decorrelated XX T )]()([ttEHxxTTTTT = T ):1(:,):1(:,):1(:,):1(:, XXX X Q x is symmetric and lag provides new information if the sources have distinct autocorrelation. is set to 5 empirically. Non-Gaussian and independent XX T xxHTxxHHEETraceERRxxxxRRxxxx][][)(][* Q x is the sum over 4 th order cumulants. 22

PAGE 33

CHAPTER 3 RESULTS This chapter discusses and compares the quality of the fetal ECG obtained by each of the three algorithms explained in the previous chapter viz MeRMaId, Generalized Eigenvalue Decomposition and the Cauchy Schwartz based quadratic mutual information minimization method. The algorithms are applied on two different data sets. First to see if the algorithms work for the particular application of fetal ECG extraction, they are tested with the normal ECG data of pregnant mother. Then, to see how the algorithms perform during the uterine contractions of the mother, they are tested with the noisy ECG data of the mother during the contractions. It has to be noted that all the ICA algorithms suffer from the problem of scale and permutation i.e. we can never know which output channel corresponds to the signal of interest (here the fetal ECG). Also we need to come up with a criterion which measures the quality of the signal of interest. So there arises a need to make use of some automated algorithms which automatically detect the presence of the signal of interest as well as assess the quality of it. The results obtained for the data during contractions are compared qualitatively using a criterion called the trust factor [19]. This trust factor varies from 0 to 1, the higher value it has the better will be the quality of the fetal ECG. The next section tells more about the data collection procedure and the following sections deal with the results of various algorithms for normal ECG data as well as for the ECG data during the contractions. Finally the section on the qualitative comparison of the results using the trust factor concludes the chapter. 23

PAGE 34

24 Data Collection The ECG data [20] is collected non-invasively using ten surface electrodes positioned on the maternal abdomen in a standard arrangement (Figure 3-1). Electrode position was systematically varied in a preliminary study on 11 patients, until the following optimal array positioning was identified: 10 electrodes encircling the maternal abdomen, with reference electrodes located centrally and on the right leg. This standard position is slightly modified for every patient due to the presence of other monitoring equipment placed on the maternal abdomen (Tocodynamometer and Ultrasonic belts). Four of the electrodes also collect EHG signals. Figure 3-1: Position of the electrodes on the pregnant woman The recorded signals are fed to an 8-channel high resolution (gain of 4000), low-noise unipolar amplifier specifically designed for FECG signals. All eight signals were measured with respect to a reference electrode. The amplifier also uses a driven right leg (DRL) circuitry to reduce common mode noise between the patient and the amplifier common. The amplifier 3dB bandwidth is 0.1 Hz and 100 Hz, with a 60 Hz notch. The

PAGE 35

25 amplifier has a variable gain, but here the gain is set to 6,500. The data are then transferred to a PC via an A/D card which has a sampling frequency of 200Hz and resolution of 16 bits. Performance of the Algorithms on Normal ECG Data MeRMaId Algorithm The MeRMaId algorithm is first applied to a normal ECG data set collected from a pregnant mother. The ECG is generally measured by placing eight electrodes on various places of the mothers abdomen and thorax. So the data will be eight dimensional as shown in figure 3-2. For the present research, all eight channels have been considered. In each channel, 10,000 samples of data are considered. Since the sampling rate is 200Hz, this corresponds to 50 seconds of the ECG monitoring. Preprocessing is done by passing the data through a second order FIR filter which has zeros at DC and near Nyquist frequency. This is done to remove the DC bias present in the signal as well as the high frequency noise. The stochastic information gradient (SIG) version [21] of the algorithm has been used. The SIG can be used to modify the MeRMaId criterion such that the complexity is reduced to O(L) from O(L 2 ). The information potential given in (2-12) can be represented as: )]([)()(1yfEdyyfYVYYY (3-1) Dropping the expectation and stochastically approximating the value of the information potential with the instantaneous value of its argument, we get )()( ~ 1kYyfYV (3-2) So the Renyis Quadratic marginal entropy in (2-12) reduces to:

PAGE 36

26 12,2)2),()((1log)(kLkjdddkRjykyGLyH (3-3) The various parameters for this algorithm are set like this: alpha = step size is set to 0.01 L = window size is set to 200 rep = number of repetitions is set to 1(since we are using SIG) stp = order of difference equation (1 D^stp) is set to 1 sig = standard deviation for Gaussian distribution (used for Parzen windows) is set to 0.25 The outputs (whose Renyis Mutual Information has been minimized) obtained for this clean data set are shown in figure 3-3. It can be clearly seen from this figure, that the mother ECG and the fetal ECG signals are well separated. In this figure, the output channels 1 and 2 represent the maternal ECG signals, channel 3 represents fetal ECG signal and the rest of the channels represent the noise.

PAGE 37

27 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5x 104 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5x 104 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -2 0 2x 104 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -2 0 2x 104 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -2 0 2x 104 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -2 0 2x 104 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5x 104 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -2 0 2x 104 Figure 3-2: Eight channels of normal ECG data. Only 2000 samples of the ECG data are shown in the figure.

PAGE 38

28 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -10 0 10 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -10 0 10 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5 MECG MECG FECG Figure 3-3: Output signals for the MeRMaId algorithm. The nature of the eight signals is mentioned to the left. Cauchy Schwartz based Quadratic Mutual Information The blind source separation problem is now accomplished using the minimization of Cauchy Schwartz (CS) based Quadratic Mutual Information (QMI). To make this algorithm work for the real ECG data, we need to know how to change the kernel size so that we can get good results. To test if the algorithm separates the sources successfully, let us first deal with 2 dimensional speech data which are mixed artificially with a known mixing matrix. The weight matrix, the final value of which will represent the demixing matrix, is initially chosen as the identity matrix. The kernel size is linearly decreased for the first 150 iterations and for the next 150 iterations its value (the value at the end of the 150 th iteration) is fixed. The step size as well as the momentum learning constant is chosen as a function of the kernel size, so that we can have larger updates when the

PAGE 39

29 kernel size is larger and smaller updates when the kernel size decreases. The signal to interference ratio is shown below in figure 3-4. Defining Signal to Interference Ratio (SIR) as 2210))(max()(maxlog10)(iTiiiOOOOiSIR (3-4) where O = W*A = product of mixing matrix and current estimate of demixing matrix and O i represents the i th row of matrix O. It can be clearly observed that very high SIR (as high as 50 dB) can be achieved for this 2 dimensional case. The learning curve which indicates how the cost function (here the Cauchy Schwartz based Quadratic Mutual Information) varies as the iterations proceed is shown in figure 3-5. 0 50 100 150 200 250 300 0 10 20 30 40 50 60 70 80 IterationsSIR Figure 3-4: Plot of the signal to interference ratio versus the iterations

PAGE 40

30 0 50 100 150 200 250 300 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 IterationsCost Function Figure 3-5: Learning curve Let us now try this algorithm on the normal ECG data. Since estimating the joint pdf of finite data samples is easy to estimate accurately in lower dimensional space, only four channels (out of the eight) of the ECG data is considered. The weights are initialized as the identity matrix as before. The number of iterations on the data is chosen as 500. In order to make the algorithm escape local minima, kernel annealing (described in chapter 2) is done. For half the number of iterations, kernel annealing is done (kernel size is gradually decreased linearly from a large value to a predetermined smaller value). For the next half the number of iterations, the kernel size is fixed. The results for this four dimensional data are shown in figure 3-6. It can be clearly seen that fetal ECG can be easily separated and is observed in channel 3 of the output.

PAGE 41

31 0 200 400 600 800 1000 1200 1400 1600 1800 -2 0 2 0 200 400 600 800 1000 1200 1400 1600 1800 -0.2 0 0.2 0 200 400 600 800 1000 1200 1400 1600 1800 -0.5 0 0.5 0 200 400 600 800 1000 1200 1400 1600 1800 -5 0 5 MECG FECG Figure 3-6: Output signals for CSBased QMI Minimization Generalized Eigenvalue Decomposition Algorithm The same data (8 by 10000 samples) is applied as input to this algorithm. All the three different assumptions (non-stationary, non-white and non-Gaussian) on the data are tried out. It can be seen from the results shown in figures 3-7, 3-8 and 3-9, that we can successfully separate the fetal ECG signal and the mother ECG signal from the input data. The channels representing the signals are shown labeled on the left in these figures. Let us now come to the parameters chosen for each of the three assumptions. The stationarity length parameter t for the non-stationary assumption case is chosen as 120 samples. The parameter for the non-white assumption is set to 5. There are no parameters for the non-Gaussian assumption.

PAGE 42

32 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.1 0 0.1 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.5 0 0.5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.5 0 0.5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.5 0 0.5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1 0 1 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1 0 1 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -2 0 2 Non Stationary 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1 0 1 MECG MECG FECG Figure 3-7: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition method using non-stationary Assumption

PAGE 43

33 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1000 0 1000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -2000 0 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -2000 0 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1 0 1x 104 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5000 0 5000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 Non White 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1000 0 1000 MECG MECG FECG Figure 3-8: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition method using non-white assumption

PAGE 44

34 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -2000 0 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5000 0 5000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -2000 0 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1 0 1x 104 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1000 0 1000 Non Gaussian 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -2000 0 2000 MECG MECG FECG Figure 3-9: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition method using non-gaussian assumption Performance of the Algorithms on the Data during Contractions Figure 3-10 shows the nature of the input data during contractions. Due to the presence of the ElectroHysteroGram (EHG) signal, the ECG data is noisier. We now attempt to separate the fetal ECG signal from eight channels of such data. The output signals obtained from the MeRMaId, the three different cases of the generalized eigenvalue decomposition algorithm are shown in figures 3-11, 3-12, 3-13, 3-14 respectively. It can be visually observed from these plots, that the MeRMaId algorithm totally fails to extract the fetal ECG. The quality of the extracted fetal ECG is comparatively better for the Generalized Eigenvalue Decomposition method based on non-white assumption. We will deal with the comparison more rigorously and qualitatively in the next section. The Cauchy-Schwartz based Quadratic Mutual

PAGE 45

35 Information minimization method failed to extract the fetal ECG from the 8 dimensional ECG data during the contractions. The reason is considered to be more due to the dimensionality of the data rather than due to the nature of the data. This problem with high dimensionality of the data is not an issue with the MeRMaId algorithm since only marginal pdfs are estimated in this algorithm (no need to estimate the joint) whereas CS-QMI has this additional problem of estimating the joint pdf in higher dimensional space. 0 0.5 1 1.5 2 2.5 3x 104 -4000 -2000 0 2000 4000 6000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 -4000 -2000 0 2000 4000 6000 Figure 3-10: One channel of ECG data during uterine contractions. The figure shown at the bottom zooms on the portion of the signal containing contractions.

PAGE 46

36 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -10 0 10 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -10 0 10 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5 MerMaid 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5 MECG MECG FECG Figure 3-11: Output signals for the MeRMaId algorithm

PAGE 47

37 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.5 0 0.5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.5 0 0.5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.5 0 0.5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.5 0 0.5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.5 0 0.5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.5 0 0.5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -5 0 5 Non Stationary Assumption 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -10 0 10 MECG MECG FECG Figure 3-12: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition method using non-stationary assumption

PAGE 48

38 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1000 0 1000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1 0 1x 104 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1000 0 1000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 Non White Assumption 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 FECG MECG MECG Figure 3-13: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition method using non-white assumption

PAGE 49

39 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1000 0 1000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1 0 1x 104 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -2 0 2x 104 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 Non Gaussian Assumption 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -500 0 500 FECG MECG MECG Figure 3-14: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition method using non-gaussian assumption Comparison of the Performance of the Algorithms In order to compare the performance of these algorithms, a criterion called trust factor [19] is defined which measures the quality of fetal ECG. This is based on the PanTompkins online QRS detection algorithm [22]. The output signals from the ICA algorithms are first passed through a band pass filter in order to remove the interfering noise. The outputs of this filter are differentiated and squared. This is followed by an integration stage realized using a moving average filter. Then thresholds are set to locate the peaks, which essentially gives the beat to beat heart rate. Different thresholds are set to determine maternal heartbeat and fetal heartbeat. The quality of the fetal ECG is judged based on the number of false positives (peaks observed when none are there actually) and on the number of false negatives (no peaks observed when there are actual

PAGE 50

40 peaks). This is determined by measured the interval between any two consecutive peaks. If this interval is less than 70% of the 5 previous RR intervals average, then there is a false positive. If this interval is more than 130% of the 5 previous RR intervals average, then there is a false negative. Based on these false positives and false negatives, a criterion is developed, called the Trust Factor, to judge the quality of the fetal ECG. The Trust Factor goes from 0 to 1 and uses several characteristics of ECG signals including: The quasi periodicity of the signal The sparseness of the signal (or the ECG-look) calculated with the number of points below a certain threshold or the kurtosis of the signal The level of noise in the signal (which is calculated by two different methods: an estimation of the false negatives and false positives, and a signal to noise ratio in the autocorrelation function) The location of the QRS peaks The performance of the algorithms for normal ECG data is compared using the Trust Factor. A window of data containing 8 channels of 10000 samples is considered for the algorithms MeRMaId, Generalized Eigenvalue Decomposition (GED) based on Non Stationary (NS) assumption, Generalized Eigenvalue Decomposition (GED) based on Non White (NW) assumption and Generalized Eigenvalue Decomposition (GED) based on Non Gaussian (NG) assumption. The data from the same window by of size 4 by 2000 is considered for the Cauchy Schwartz (CS) based Quadratic Mutual Information (QMI) algorithm. The values for the Trust Factor for each algorithm are shown in table 3-1. To compare the performance of these algorithms during the contractions, five windows each containing 10000 samples of the eight dimensional data is considered and each algorithm is applied to it. The resulting value of the trust factor is shown in the table

PAGE 51

41 3-2. The results for CS-QMI are not presented for this data set since the algorithm failed to extract the fetal ECG (reasons mentioned earlier in the chapter) while dealing with this dataset. Table 3-1. Comparison of performance of the BSS algorithms for normal ECG Trust Factor Window Number MeRMaId GED NS GED NW GED NG CS-QMI 1 0.7747 0.7640 0.7115 0.7983 0.4859 Table 3-2. Comparison of performance of the BSS algorithms for ECG data during contractions Trust Factor Window Number MerMaid GED NS GED NW GED NG 1 0.1975 0.2180 0.3823 0.3002 2 0.3996 0.5036 0.5261 0.4692 3 0.6375 0.4806 0.5690 0.5830 4 0.7306 0.7162 0.6521 0.5424 5 0.6752 0.7214 0.6348 0.6072 Mean 0.5281 0.5280 0.5528 0.5004

PAGE 52

CHAPTER 4 CONCLUSIONS AND FUTURE WORK Conclusions All the three algorithms BSS using MeRMaId, BSS using Generalized Eigenvalue Decomposition (GED) BSS using Cauchy Schwartz (CS) based Quadratic Mutual Information(QMI) are used to extract the fetal ECG from two different data sets :normal ECG recordings and ECG recordings during the uterine contractions of a pregnant woman. From the results presented in chapter 3 the following conclusions can be drawn: 1. MeRMaId The MeRMaId algorithm extracts the fetal ECG from the normal ECG data and the quality of the extracted fetal ECG is quite good. However, this algorithm fails to give good quality fetal ECG when dealing with the ECG data during the contractions. The reason for this poor performance can be attributed to the spatial pre-whitening step performed on the observations, which worsens the already poor SNR. 2. GED The GED algorithm, based on all the three assumptions on the data, non-stationary, non-white, non-Gaussian, gives a high quality fetal ECG from the normal ECG data. On the data during the contractions, the nonwhite assumption gives the best performance in terms of the quality of fetal ECG as measured by the criterion given by [20]. The non-stationary assumption gives results slightly superior to that of the MeRMaId while the non-Gaussian assumption gives results slightly worse than the MeRMaId algorithm. 42

PAGE 53

43 3. CS QMI This algorithm gives very promising results for lower dimensional data as illustrated by the blind source separation of a 2 dimensional speech data which is artificially mixed. But the algorithm suffers in performance as the dimensionality of the data is increased. To test the performance on the normal ECG data, only 4 (out of 8) channels are considered. The algorithm gives a good quality fetal ECG using these 4 channels only. But the data during the contractions, being noisier, inherently has more independent sources. So there arises the need to use all the 8 channels which makes the algorithm give poor results (no fetal ECG is observed). Scope for Future Work There are a couple of ideas, which researchers have successfully used to solve the blind source separation problem. These methods are particularly appealing for the ECG data which we have dealt with. Zibulevsky and Pearlmutter [23] exploited the property of the sources having a sparse representation in a signal dictionary for blind source separation and obtained very promising results. The dictionary may consist of wavelets, wavelet packets or coefficients in any other domain where they are sparse. The ECG signals can be considered to be having a sparse distribution in time since the active portions in the signal last only for a small amount of time. But the presence of noise (especially during the contractions) makes this assumption of sparse sources to be weak. But if we can have a denoising algorithm which improves the SNR significantly, then we can expect a superior performance by this algorithm for this application. Least dependent component based on Mutual Information (MILCA) proposed by Stogbauer et al [24] is very interesting in the sense that they take into account the time

PAGE 54

44 structure of the signal while doing a blind source separation. In this work, they propose to use a Mutual Information (MI) estimator based on k-nearest neighbor statistics [23]. Using this estimate of MI, they find the least dependent components in a linearly mixed signal. The fact that we are finding only the least dependent components instead of independent components is very useful for the problem of fetal ECG extraction because the fetal heartbeats and mother heartbeats are not entirely independent. By making use of the time structure and higher order statistics we can obtain optimal results in general. By delay embedding the observable signals (here non-invasive measurements of a pregnant mother), promising results have been obtained. This method of minimizing the mutual information of the delay embedded signals will give outputs which are least dependent. It would be really interesting to apply this method to the ECG recordings during contractions and minimize the k-nearest neighbor estimate of MI (if not Renyis MI).

PAGE 55

LIST OF REFERENCES 1. Bernard Widrow, Samuel D Stearns: Adaptive Signal Processing, Prentice Hall Inc., Upper Saddle River, NJ, 1985. 2. G Camps, M Martinez, E Soria: Fetal ECG Extraction using an FIR Neural Network, Computers in Cardiology, 23-26 September 2001. 3. F Mochimaru, Y Fujimoto: Detecting the Fetal Electrocardiogram by Wavelet Theory-Based Methods, Progress in Biomedical Research, Vol.7, No.2, September 2002. 4. S Mallat, W L Hwang: Singularity Detection and Processing with Wavelets, IEEE Transactions on Information Theory, Vol. 38, Issue. 2, pp. 617-643, March 1992. 5. V Vigneron, A Paraschiv-Ionescu, A Azancot, O Sibony, C Jutten: Fetal Electrocardiogram Extraction Based On Non-Stationary ICA And Wavelet Denoising, Proceedings Seventh International Symposium on Signal Processing and Its Applications, Vol. 2, pp. 69-72 1-4, July 2003. 6. D T Pham, J F Cardoso: Blind Separation of Instantaneous Mixture of Non-Stationary Sources, IEEE Transactions on Signal Processing, 49(9), pp. 1837-1848, 2001. 7. K S Tang, K F Man, S Kwong, Q He: Genetic Algorithms and their Applications, IEEE Signal Processing Magazine, Vol. 13, Issue. 6, pp. 22-37, November 1996. 8. S Horner, W Holls, P B Crilly: Non-invasive Fetal Electrocardiograph Enhancement, Proceedings of Computers in Cardiology, pp. 163-166, 11-14 October 1992. 9. A Kam, A Cohen: Detection of Fetal ECG With IIR Adaptive Filtering and Genetic Algorithms, IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol. 4, Pages.2335 2338, 15-19 March 1999. 10. Allan Kardec Barros, Andrzej Cichocki: Extraction of Specific Signals with Temporal Structure, Neural Computation, Vol. 13, Issue. 9, September 2001. 11. Kenneth E Hild II, Deniz Erdogmus, Jose Principe: Blind Source Separation Using Renyis Mutual Information, IEEE Signal Processing Letters, Vol. 8, No. 6, June 2001. 45

PAGE 56

46 12. Dongxin Xu, Jose C Principe, John Fisher III, Hsiao-Chun Wu: A Novel Measure for Independent Component Analysis (ICA), ICASSP, Vol. II, pp. 1161-1164, 1998. 13. Lucas Parra, Paul Sajda: Blind Source Separation via Generalized Eigenvalue Decomposition, Journal of Machine Learning Research 4, pp. 1261-1269, 2003. 14. A. Renyi: Probability Theory, Amsterdam, The Netherlands, North Holland, 1970. 15. Jose C Principe, Dongxin Xu: Information Theoretic Learning using Renyis Quadratic Entorpy, International Conf. on ICA and Signal Separation, pp. 407-412, August 1999. 16. Jose C Principe, Dongxin Xu, John W Fisher III: Information Theoretic Learning, Book Chapter in Unsupervised Adaptive Filtering, John Wiley & Sons, Inc., New York, NY, 2000. 17. L. Molgedey, H.G. Schuster: Separation of a Mixture of Independent Signals Using Time Delay Correlations, Physics. Review. Letters. 72, Issue. 23, pp. 3634-3637, June 1994. 18. J F Cardoso, A. Souloumiac: Blind Beamforming for Non-Gaussian Signals, IEE Proceedings, Vol. 140, No. 6, December 1993. 19. Dorothee E Marossero, Deniz Erdogmus, Neil Euliano, Jose C Principe, Kenneth E Hild II: Independent Components Analysis For Fetal Electrocardiogram Extraction: A Case For The Data Efficient MERMAID Algorithm, Proceedings of NNSP'03, pp.399-408, Toulouse, France, September 2003. 20. T Y Euliano, D E Marossero N R Euliano B Ingram, K Andersen, R K Edwards: Non-invasive Fetal ECG: Method Refinement and Pilot Data, Anesthesia and Analgesia in press. 21. Kenneth E Hild II, Deniz Erdogmus, Jose C Principe: On-line Minimum Mutual Information Method for Time Varying Blind Source Separation, International Conference on ICA and Signal Separation, pp.126-131, San Diego CA, December 2001. 22. J Pan, W J Tompkins : A Real Time QRS Detection Algorithm, IEEE Transactions on Biomedical Engineering, Vol. 32, No. 3, pp. 837-843,1985. 23. Michael Zibulevsky, Barak A Pearlmutter: Blind Source Separation by Sparse Decomposition, Neural Computation, Vol. 13, Issue. 4, pp. 863-882, April 2001. 24. Harald Stogbauer, Alexander Kraskov, Sergey A Astakhov, Peter Grassberger: Least Dependent Component Analysis Based on Mutual Information, DOI: physics/0405044, arXiv, 2004.

PAGE 57

47 25. A Kraskov, H Stogbauer, P Grassberger: Estimating Mutual Information, Physics Review E, 2004.

PAGE 58

BIOGRAPHICAL SKETCH Hemanth Peddaneni received his bachelors degree in electronics and communication engineering, from Sri Venkateswara University, Tirupati, India, in 2002. He has been a Young Engineering Fellow, awarded by the Indian Institute of Science, Bangalore, India. He is now pursuing his masters degree in electrical and computer engineering at the University of Florida. His research interests include neural networks for signal processing, adaptive signal processing, wavelet methods for time series analysis, digital filter design/implementation and digital image processing. 48


Permanent Link: http://ufdc.ufl.edu/UFE0007480/00001

Material Information

Title: Comparison of Algorithms for Fetal ECG Extraction
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0007480:00001

Permanent Link: http://ufdc.ufl.edu/UFE0007480/00001

Material Information

Title: Comparison of Algorithms for Fetal ECG Extraction
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0007480:00001


This item has the following downloads:


Full Text












COMPARISON OF ALGORITHMS FOR FETAL ECG EXTRACTION


By

HEMANTH PEDDANENI













A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2004

































Copyright 2004

by

Hemanth Peddaneni















ACKNOWLEDGMENTS

Any accomplishment is possible only when there is a motivation and a guiding

force. I am highly grateful to my advisor, Dr. Jose Principe, for providing both of these.

His suggestions and encouragement have been of immense help for me in completing this

thesis.

I would like to express my gratitude to Dr. Deniz Erdogmus and Dr.

Yadunandana Rao for the many discussions we had, without which the work would not

have been completed. I would like to thank Ms. Dorothee Marossero for providing me the

ECG data sets and for her help in evaluating the performance of the algorithms.

I would like to thank Dr. Michael Nechyba and Dr. Fred Taylor for serving on my

committee.

I am thankful to my friends at CNEL, Anant, Jianwu and Can, for providing a

friendly atmosphere and lending their hand whenever I had some problems.

Finally I would like to thank my family members for their support and love,

which have been of utmost importance for me to complete the present work.
















TABLE OF CONTENTS



A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF TABLES ................................................... vii

LIST OF FIGURES ................................ ........... ............................ viii

A B S T R A C T ........................................................................................................ ............ ix

CHAPTER

1 IN TR O D U C T IO N ........ .. ......................................... ..........................................1.

P problem D description .. ................................................................................ .. 1...
P a st R e search ................................................................................................... 3
G o als of th e T h esis ... ... ........................................... ....................... .. ........... ....

2 DESCRIPTION OF ALGORITHMS STUDIED...................................................9...

B SS U sing M eRM aId A lgorithm ........................................................ ...............9...
B SS U sing M inim ization of CS QM I............................................. ............... 14
BSS Using Generalized Eigenvalue Decomposition....................................... 17

3 R E S U L T S ................................................................................................................. .. 2 3

D ata Collection .............. . .................................................. 24
Performance of the Algorithms on Normal ECG Data.....................................25
M eR M aId A lgorithm ................................... .................................................. 2 5
Cauchy Schwartz based Quadratic Mutual Information ................................28
Generalized Eigenvalue Decomposition Algorithm.......................................31
Performance of the Algorithms on the Data during Contractions ......................34
Comparison of the Performance of the Algorithms.........................................39

4 CONCLUSIONS AND FUTURE WORK............................................................42

C o n c lu sio n s ....................................................................... ..................................... 4 2
Scope for Future W ork .......................................... ......................... ................ 43

L IST O F R E FE R E N C E S ... ........................................................................ ................ 45









BIO GR APH ICAL SK ETCH .................................................................... ................ 48
















LIST OF TABLES


Table page

2-1. Summary of procedures for BSS using Generalized Eigenvalue Decomposition
(G ED ) for fetal E C G extraction ........................................................... ................ 21

3-1. Comparison of performance of the BSS algorithms for normal ECG....................41

3-2. Comparison of performance of the BSS algorithms for ECG data during
c o n tra ctio n s .............................................................................................................. 4 1















LIST OF FIGURES


Figure page

3-1: Position of the electrodes on the pregnant woman.............................. ................ 24

3-2: Eight channels of normal ECG data. Only 2000 samples of the ECG data are
shown in the figure......................... ........... .........................27

3-3: Output signals for the MeRMaId algorithm. The nature of the eight signals is
m mentioned to the left. ............. ................ .............................................. 28

3-4: Plot of the signal to interference ratio versus the iterations ................................29

3 -5 : L earn in g cu rv e .......................................................................................................... 3 0

3-6: Output signals for CS- based QM I M inimization ............................... ................ 31

3-7: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition
m ethod using non-stationary assum ption............................................. ................ 32

3-8: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition
m ethod using non-w hite assum ption ................................................... ................ 33

3-9: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition
method using non-gaussian assumption..................................................... 34

3-10: One channel of ECG data during uterine contractions. The figure shown at the
bottom zooms on the portion of the signal containing contractions......................35

3-11: Output signals for the M eRM aId algorithm ....................................... ................ 36

3-12: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition
m ethod using non-stationary assum ption............................................. ................ 37

3-13: 2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition
m ethod using non-w hite assum ption ................................................... ................ 38

3-14:2000 samples of the outputs signals for the Generalized Eigenvalue Decomposition
m ethod using non-gaussian assumption..................................................... 39















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

COMPARISON OF ALGORITHMS FOR FETAL ECG EXTRACTION

By

Hemanth Peddaneni

December 2004

Chair: Jose Principe
Major Department: Electrical and Computer Engineering

The thesis addresses the extraction of the fetal ECG signal from the non-invasive

ECG measurements of a pregnant woman. This is an ideal situation for independent

component analysis because the assumption that the two sources in the measurements,

fetal ECG and mother ECG, are independent is verified at the short time scale used for

separation.

Three algorithms, Blind Source Separation using Minimum Renyi's Mutual

Information, using Generalized Eigenvalue Decomposition and using Cauchy Schwartz

Quadratic Mutual Information Minimization, have been used to get the fetal ECG under

normal conditions and during the uterine contractions of the mother. Minimum Renyi's

Mutual Information method uses whitening of the data and as such it is less suitable to

extract the fetal ECG during contractions. The Generalized Eigenvalue Decomposition

method turned out to give superior quality of the fetal ECG during the contractions. The

third method, Cauchy Schwartz Quadratic Mutual Information Minimization, gave









promising results for lower dimensional normal ECG data but failed to work for the

higher dimensional ECG data during contractions.

The quality of the extracted fetal ECG is compared using a criterion called Trust

Factor (which varies from 0 to 1, 1 corresponds to the best quality). These results help in

determining which algorithm is best suited for finding the fetal heart rate since the QRS

complex is preserved in all three algorithms.














CHAPTER 1
INTRODUCTION

Fetal electrocardiogram (fetal ECG) extraction is an interesting as well as a difficult

problem in signal processing. This forms one important application of Independent

Component Analysis (ICA) or Blind Source Separation (BSS), where one wants to

separate mixtures of sources with very little prior information. In this chapter we will first

describe the problem description followed by the past research that has been done in this

area and then finally about the goal of this thesis.

Problem Description

Fetal electrocardiogram monitoring is a technique for obtaining important

information about the condition of the fetus during pregnancy, by measuring the

electrical signals generated by the fetal heart as measured from multi-channel electrodes

placed on the mother's body surface. This method of recording the fetal ECG from the

mother's body, without direct contact with the fetus (which is highly desirable) is called

non-invasive method. However, in this method of recording, the fetal ECG signals have a

very low power relative to that of the maternal ECG. In addition, there will be several

sources of interference, which include intrinsic noise from a recorder, noise from

electrode-skin contact, baseline drift (DC shift), 50/60 Hz noise etc. The situation is far

worse during the uterine contractions of the mother. During these contractions, the ECG

recordings will be corrupted by other electrophysiological signals called uterine

electromyogram (EMG) or electrohysterogram (EHG), which are due to the uterine

muscle rather than due to the heart. The response of the fetal heart to the uterine










contractions is an important indicator of the fetal health. As such a need arises to

effectively monitoring the fetal ECG during the uterine contractions. But monitoring the

fetal ECG during these contractions is a difficult task because of very poor SNR. The

nature of these contractions is shown in figure 3-7 of chapter 3.


4000 1


T


60 80 100


Figure 1-1: Components of the ECG waveform

The nature of the fetal ECG is similar to that of mother ECG signal and is shown

in figure 1-1. The ECG waveform is also called PQRST wave. The first waveform in the

ECG-the P wave-is due to the atrial contraction. The next waveform-QRS complex-is

due to the ventricular contraction. The final waveform is the T wave which occurs as the

heart prepares for the next heartbeat. The location of P, Q, R, S and T components are

indicated in the figure 1-1. The three main characteristics that need to be obtained from

the fetal ECG extraction for useful diagnosis include









Fetal heart rate

Amplitude of the different waves

Duration of the waves.

But because of the non-invasive nature of measurement of the fetal ECG, most of the

signal processing algorithms detect only the R waves and the P and T waves will usually

remain hidden.

Also fetal ECG extraction problem is not easily solved by conventional filtering

techniques. Linear filtering in the Fourier domain fails since the spectral content of all the

three components, maternal ECG, fetal ECG and noise are rather similar and overlap.

Past Research

The problem of fetal ECG extraction was tackled more than 30 years ago by means

of now conventional adaptive noise canceling techniques. Widrow and Stearns [1] used a

linear adaptive filter framework to cancel the mother ECG and obtain the fetal ECG.

They used two sets of electrodes, one set placed on the abdomen of the mother and the

other placed on the chest of the mother. The electrodes placed on the abdomen pick up

both the fetal ECG and mother ECG (serve as primary inputs), whereas the electrodes

placed on the chest pick up only the mother ECG (serve as reference inputs). So by

having the signals from the electrodes placed on the abdomen as desired and the signals

from the electrodes placed on the limbs as input to the adaptive filter, the error signal can

be made to represent the extracted fetal ECG. This method although providing a solution,

is not robust enough to be used for clinical practice. First one needs to have more

electrodes to measure the signals. Second, if the amplitude of the background noise is

greater than the fetal heartbeat, as is the case generally during the uterine contractions,









the resulting error signal will not contain the fetal ECG. This method fails to extract the

fetal ECG when both the mother and fetal ECG overlap. Further more, if there is leakage

of the fetal ECG into the recordings of the reference input (mother ECG), the quality of

the extracted fetal ECG will be extremely poor. The positioning of the abdominal

electrodes is extremely critical to get a good fetal ECG. They will have to be placed at

places on the mother where maximum amount of fetal ECG is picked up (again this leads

to the issue of where to place the electrodes). Also in this framework, only second order

statistics are used and higher order statistics are ignored.

Camps et al. [2] also used an adaptive noise canceling technique to extract the fetal

ECG but with the linear adaptive filter replaced with a time delay neural network

(TDNN). This TDNN is nothing but an artificial neural network (like a multilayered

perception) with the synaptic weights replaced by FIR filters. This is done to provide

highly non-linear dynamic capabilities to the fetal ECG recovery model. They trained the

network using temporal backpropagation. Again this method suffers from the same

difficulties mentioned earlier. In addition training this neural network is not easy and is

extremely computationally expensive. Care should be taken to decide on proper

initialization of the weights, number of hidden neurons, taps per neuron in a layer and

learning rate.

Mochimaru and Fujimoto [3] used wavelet based methods to detect the fetal ECG.

They used multiresolution analysis (MRA) to remove the large baseline fluctuations in

the signal as well as to remove the noise. MRA was performed on the raw ECG data up

to the 12th level using Daubechies20 wavelets. The 12th order approximation function

consists of slow variations of the signal. This was subtracted from the original raw signal









to get a signal free from baseline fluctuations. To remove the noise, they applied wavelet

transform based denoising of the detrended data by multiresolution analysis up to the 12th

level using Coiflet24 wavelets. Noise removal was accomplished by thresholding the

wavelet coefficients at each level. Weighted standard deviation of the wavelet

coefficients at each resolution level were used as the thresholds at each resolution level.

The fetal ECG was monitored by calculating the Lipschitz exponent [4]. The main

problem with this method is its inability to locate the fetal ECG if it is obscured by the

mother ECG. Since this happens two or three times in a 10 seconds period, it can be a

major drawback. Also there is a need to set the thresholds on the wavelet coefficients

dynamically during denoising, since the noise content is more during the uterine

contractions. Again the performance of this type of denoising during the contractions

may not be optimum since thresholding of the wavelet coefficients may result in

removing the fetal ECG component altogether in the original signal.

Vigneron et al. [5] applied blind source separation methods for fetal ECG

extraction by (i) exploiting the non-stationarity of fetal ECG and (ii) implementing post

denoising using wavelets. The blind source separation algorithm proposed by Pham and

Cardoso [6] was made use here. This algorithm minimizes the Gaussian mutual

information, defined as the ordinary mutual information with respect to some Gaussian

random vectors with the same covariances structure as the random vector of interest, to

get the independent components in the signal. Then the wavelet transform was used to

remove the baseline drift in the extracted noisy fetal ECG signal. After that, the PQRST

of the fetal ECG is amplified by using a non-linear filtering technique. After PQRST

amplification, a wavelet denoising is applied to the fetal ECG signal with the following









parameters: biorthogonal wavelet type, level 6 decomposition and the data adaptive

threshold selection rule 'SureShrink' of MATLAB wavelet toolbox. The problem with

this method is that there are too many post processing stages, as such lot of parameters (

like choice of non-linear filters, wavelet for baseline removal as well as denoising, level

of decomposition etc.) need to be determined empirically.

Work has also been done to extract the fetal ECG using genetic algorithms [7]. The

genetic algorithm approach for fetal ECG extraction, proposed by Horner et al. [8], is

based on subtracting a pure maternal ECG from an abdominal signal containing fetal and

maternal ECG signals. Subtraction via a Genetic Algorithm is supposed to be near

optimal rather than a straight subtraction. The issue with this method is the need to get

the maternal ECG signals whose shape is similar to the maternal ECG present in the

abdominal recordings (which contain fetal ECG). So it needs to be determined exactly,

where the electrodes need to be placed to pick up the maternal ECG alone. Kam and

Cohen [9] proposed two architectures for the detection of fetal ECG. The first is a

combination of an IIR adaptive filter and Genetic Algorithm, where the Genetic

Algorithm is recruited whenever the adaptive filter is suspected of reaching local minima.

The second is an independent Genetic Algorithm (GA) search without the adaptive filter.

The main disadvantage of an IIR filter is that the error surface is not quadratic but a multi

modal surface. So the presence of the genetic algorithm forces the algorithm to overcome

the local minima and reach the global solution. The quality of the extracted fetal ECG

using this IIR-GA adaptive filter is superior to that obtained using the GA alone. This

method of combining an adaptive filter with a genetic algorithm is interesting and it









would be nice to see how it performs when there are uterine contractions in the ECG

data.

Barros and Cichocki [10] proposed a semi-blind source separation algorithm to

solve the fetal ECG extraction problem. This algorithm requires a priori information

about the autocorrelation function of the primary sources, to extract the desired signal

(fetal ECG). They do not assume the sources to be statistically independent but they

assume that the sources have a temporal structure and have different autocorrelation

functions. The main problem with this method is that if there is fetal heart rate variability,

as is the case when the fetus is not healthy, the a priori estimate of the autocorrelation

function of the fetal ECG may not be appropriate.

Goals of the Thesis

The following are the goals of the thesis:

Assess the performance of BSS algorithms that use whitening of data as a
preprocessing step.

Use Cauchy-Schwartz based Quadratic Mutual Information minimization to
extract the fetal ECG.

Under varying assumptions on the data, use Generalized Eigenvalue
Decomposition to solve the blind source separation problem.

Compare the performance of BSS algorithms which include whitening and which
do not include whitening.

The rest of the thesis is organized as follows. Chapter 2 provides a detailed

description about the algorithms which were studied to solve the fetal ECG extraction

problem. Chapter 3 describes the results obtained using the algorithms presented in

Chapter 2. Finally Chapter 4 concludes the thesis by making observations on the results







8


described in Chapter 3, along with some suggestions for future research in this particular

area.














CHAPTER 2
DESCRIPTION OF ALGORITHMS STUDIED

The extraction of the fetal ECG signal from the ECG recording of a pregnant

mother has been carried out using three different algorithms. The MeRMaId (Minimum

Renyi's Mutual Information) algorithm for Blind Source Separation (BSS) proposed by

Hild et al. [11], whitens the input data spatially before minimizing the Renyi's Mutual

Information between the outputs. The algorithm proposed by Xu et al. [12] performs

BSS by minimizing the 'Cauchy-Schwartz quadratic mutual information' (CS QMI) of

the outputs. The BSS via Generalized Eigenvalue Decomposition proposed by Parra and

Sajda [13] provides an elegant way of finding the demixing matrix using generalized

eigendecomposition of the covariance matrix and an additional symmetric matrix (which

depends on the type of assumption made).These three algorithms along with some of the

practical aspects in implementing them for the fetal ECG extraction are described in

detail in this chapter.

BSS Using MeRMaId Algorithm

sn Y (xn) (n) y (n)

Mixing Whitening Rotation
Matrix Matrix Matrix
__ A W R

Figure 2-1: Block Diagram for two sources/observations

The above figure depicts the overall block diagram of the MeRMaId algorithm.

The source signals represented by s (n) are assumed to be independent. These signals are

mixed by an unknown mixing matrix A to get the observable signals x (n). This









observable data is first decorrelated spatially by applying a whitening transform (more

will be described about this later in the chapter). Once whitening has been done, the

problem of finding the independent components reduces to a simple rotation. So we need

to find a rotation matrix which minimizes the Renyi's Quadratic Mutual Information.

Let us provide some mathematical aspects of the whitening technique. The

observable data x (n) can be written as x (n) = As (n). Let (n) represent the whitened

data and dropping the index of time n for the sake of convenience, then

x= Wx
Ef J \ (2-1)

(2-1) turns out to be

WRxWT = I= Rx-1/2RxRx-1/2 (2-2)

Comparing, the RHS and LHS of (2-2), we get,

W = Rx-1/2 (2-3)

Representing, the covariance matrix in terms of its eigenvalues and eigenvectors, the

whitening transform is given by

W = VD-1/2vT (2-4)

where V is eigenvector matrix of Rx and D is the diagonal eigenvalue matrix of Rx.

Why should we do whitening? To answer this question, let us have a look at the

plot shown in figure 2-2. The figure deals with two dimensional data (for the sake of

visualization). We see that by rotating the whitened data, we can achieve the desired

solution of finding the independent components. So after whitening, the optimization

problem of minimizing the Renyi's Mutual information is constrained to a rotation

matrix.











Source Data
00. . .:. ... *.)

'." .. .. : ... ..:"".'"'. ." :;. .. ."

0 2 "*) .^ *.. .;.. t. .'. '.: .
0 01 02 03 04 05 06 07 08 09 1
Mixed Data




05

0 02 04 06 08 1 12 14
Whitened Data


h"" *" ,*% .......'



-1 -05 0 05 1 15 2 25 3 35



Figure 2-2: Effects of Whitening

The whitening operation transforms the mixing matrix A to a new one which is

orthogonal. As such, instead of estimating n2 (assuming A to be a n x n matrix)

parameters in the mixing matrix, it is sufficient if we can estimate n(n-l)/2 parameters in

the new orthogonal mixing matrix( since the number of degrees of freedom in a mixing

matrix is n(n-1)/2). So in larger dimensions, we need to estimate approximately half the

number of parameters of an arbitrary matrix. Another advantage of whitening is it

normalizes the data automatically. So we do not have to worry, even if we use scale

dependent estimators for estimating mutual information.

What's bad with whitening? The whitened data will be proportional to the power

of the input data. If the observable data is noisy (like what we have in the ECG of a

mother during uterine contractions), whitening degrades the already poor SNR by









enhancing the noise component. So it is advisable to make use of algorithms which do

not involve whitening of the data in such situations. The other two algorithms described

in this chapter does not use whitening for preprocessing the data.

Let us now go into details about minimizing the Renyi's mutual information.

Renyi's mutual information of order a [14] is defined as


IR (Y) =-- log Fn fY(Y), dy (2-5)
f- fYd(Yd ) 1
d=1

This equation can be approximated as


Sfy (y)u dy
IRa (y) l og c no (2-6)
S1 IfY d(Yd)u dyd
-oo d=1

Both (2-5) and (2-6) are nonnegative and evaluate to zero if and only if all the

outputs are statistically independent i.e. when the joint pdf is equal to the product of

marginal pdfs. As such both (2-5) and (2-6) have the same global minima and hence (2-

6) is a good approximation of (2-5), for use as a cost function in adaptation. Now (2-6)

can be written as


= log d )d + log fy(y)udy
IRa (Y) = f fYd( d d 1
d=1 -m (2-7)
n
= HR (yd) -HR(y)
d=1

So the Renyi's Mutual information of order a turns out to be approximately the

sum of Renyi's marginal entropies minus Renyi's Joint entropy of the output y. Since

y = Rx, the pdfs of y and x are related as:









f y (x)
fy (y) ) (2-8)
R

So the Renyi's Joint entropy of y becomes:


1 log f(x)
HR (yv) = 10g- Rdx




S(HR (x)+ logR


The Renyi's mutual information can now be expressed as:

n
IR (y) = HHR (yd) HR (x) log R (2-10)
d=1

Since R is purely a rotation matrix, determinant of R is one. So log|R vanishes. Also, we

have to minimize this mutual information with respect to the rotation matrix R. As the

joint entropy of x HR, (x), does not depend on R, it drops out of the cost function. The

final cost function is just the sum of the marginal entropies of the output y, i.e.,


J= ZHR, d) (2-11)
d=1

The advantage with this algorithm is that you do not have to estimate the joint

entropy at all, which is comparatively difficult than estimating the marginal entropies.

The marginal entropies can be estimated easily using the Parzen windowing with a

Gaussian kernel. The estimate of Renyi's quadratic (a=2) marginal entropy simplifies to

[15]


HR2 (Yd) = -0log2 I G(yd()-yd(k),2G2) (2-12)
N =l k=1








where G(x,2o2) is a Gaussian PDF and yd(j) is the jth sample of output yd. The argument

of the log in (2-12) is called the information potential.

BSS Using Minimization of CS QMI
In order to compare the performance of the algorithms which does pre-whitening

of the data before minimizing the Renyi's Quadratic mutual information, the BSS

problem is solved using the Cauchy-Schwartz Quadratic Mutual Information [16]. The

mutual information between two (or more) random variables can be measured using the

Kullback-Leibler divergence:

K(f, g) = f (x)log(f (x) / g(x))dx (2-13)

where f(x) and g(x) are any two pdfs. The corresponding Renyi's measure of divergence

between the two pdfs is given by the following equation:

R.(f,g) = log( (f () /g(x)-ldx (2-14)
cl -1

It can be seen that, we can integrate neither (2-13) nor (2-14) with the Parzen

windowing method to produce a simple result. But if we use the Cauchy-Schwartz

inequality to approximate the mutual information, we get the following measure:

( df((x g(x)2xdx)
C(f, g) = log( f2 dr) (2-15)
( f(x)g(x)dx)

We can easily see that, C (f,g)>0 and the equality sign holds good if and only if

f(x)=g(x). Let us now replace f(x) by the joint pdf of two random variables Y1 and Y2 and

g(x) by the product of their marginal pdf's. Now (2-15) becomes,

(,Y2 log( f12 (YY2 )2 dyldy2 )( Y fy f ()2 2 (Y2 )2 dyldy2)
C(Y, Y2 g (fY1 y 2)fY1 (Y)Y2 (y2)dYldY2)2








Now C (Yi,Y2) >0 and the equality sign hold good if and only if the joint pdf of Y

is equal to the product of its marginal pdfs. We will now see how we can integrate this

with the Parzen window method of estimating the pdf.

The joint pdf estimate of the two-dimensional random variable Y= {Yi,Y2} using

the Parzen window method is given as:


fY2 (z1, z2 ) = G(z, -yl (i),G2i)xG(z2 Y2 ( 2) (2-17)

The marginal pdf's can be estimated as:


fYd (Zd)= G(zd d(i),2) d=l1,2 (2-18)
N=1

We will make use of the fact that if G(z-a, ,1) and G(z-aj, 2)are two Gaussian

functions with means ai and aj, covariance matrices Y1 and Y2 respectively then,


fG(z -a, 1)xG(z- a, 2)= G(a,-a, (1 + 2)) (2-19)


Let us now compute the terms in the numerator and denominator of (2-16)

separately,

1^
JfY1Y2 (Y1, 2 2 dyldy2 2 G(y, (i) y (), 2 I) x G(y2 ( Y2 (j),2G21)
N =1 =l1
(2-20)

1NN
fd (yd)2dyd =--G(yd)-yd(j),2&2I) d=l1,2 (2-21)



JJfy1A2 (1, 2 )fY1 (l )fY2 (y2)dyldy2 3 1 IG(yd ()-Yd(j),2G21)
S=1 d=1 j=1

(2-22)









where n is the number of dimensions in the data (here n=2).

It can be easily seen that, the equations (2-20) through (2-22) can be easily

computed and the cost function given by (2-16) can be evaluated. Thus, Parzen

windowing can be easily integrated with the Cauchy-Schwartz based Quadratic Mutual

Information estimation.

Once the cost function (2-16) is evaluated, we can minimize it using any of the

optimization techniques. The Gradient Descent has been used in the present work. In this

the weights are initialized and they are adjusted iteratively such that the gradient of the

cost goes to zero. The weight update can be carried out as:

Wn+1 = W, r D, +a* M, (2-23)

Where

rl=step size

Dn= derivative of the cost function at time instant 'n' with respect to the weight matrix

a=momentum learning constant

Mn= (Wn+l Wn)

The momentum learning has been incorporated into this optimization method in order to

overcome the local minima to some extent. As the iterations proceed, the weight matrix

converges to, hopefully, the demixing matrix1.

The parameter which needs to be carefully chosen is the size of the Gaussian

kernel, which we are using to estimate the integrals. By choosing any arbitrary kernel and

doing the above optimization method, will not give optimal results. The method will

invariably get stuck in some local minima present in the cost function. In order to avoid


1 Up to the order of scale and sign









this, a concept called the kernel annealing has been used. Ideally, we would like our

kernel to depend on the data as well as on the number of samples in the data. This makes

sense because the same kernel size may be good for one type of data and may not be

good for other types of data. Also if you have more number of samples, we can use a

kernel with smaller variance and vice versa. These two ways of choosing the kernel size

have been incorporated in the following way.

1. Choose the kernel size as the average of the standard deviations of the data
in each dimension.

2. Scale this kernel size down by the square root of the number of samples of
data.


Coming to the kernel annealing part, we will start with a large kernel size. Then

all the data samples are just like one sample compared to the kernel size. So the estimated

pdf will be just like one Gaussian and the landscape of the cost function will be very

smooth. Then as we gradually reduce the kernel size (in this case linearly), the landscape

of the cost function becomes rough with multiple peaks and valleys. For half the number

of iterations, we will decrease the kernel size and for the other half of the iterations we

will search for the solution with the minimum kernel size (fixed) we have chosen. As a

result of this the algorithm may escape the local minima and converge to the global

minima.

BSS Using Generalized Eigenvalue Decomposition

Let s(t) represent n-dimensional sources, on which we impose certain assumptions

(more on these assumptions later). Let x(t) represent the observable signals. If A is the

mixing matrix, which is unknown, then x(t) = As(t).









The mixing matrix explains the various cross statistics of the observations x(t) as

an expansion of the corresponding diagonal cross statistics of the sources s(t). Let Rs and

Rx denote the covariance matrices of s (t) and x (t). Then,

Rx = E[x(t)xH (t)] = AR,AH 2 (2-24)

If the sources are assumed to uncorrelated, then the source covariance matrix Rs is

diagonal. Let us also assume, in addition to the covariance matrix, there exists other cross

statistics matrix represented by Qs that has the same diagonalization property i.e.

Qx = AQAH (2-25)

It is also assumed that Qs has non-zero diagonal values, which ensures the

existence of Qs,1. Let W be the demixing matrix, which we want to determine, such

that WHA = I. Now multiplying both sides of (2-24) by W, we get,

RW = AR, (2-26)

Multiplying (2-25) by W and then by Qs,1, we obtain

QxWQ 1 = A (2-27)

Substituting (2-27) in (2-26),

RW = QxWQ~ Rs (2-28)

Since both Qs-' and Rs are diagonal, their product is also diagonal. Letting Q Rs = A,

where A is also diagonal,

RxW = QxWA (2-29)




2 We are assuming that x(t) and s(t) are complex valued variables. For real valued variables, Hermetian(H)
turns out to be the same as Transpose(T)









(2-29) represents a generalized eigenvalue equation, where W and A represent the

generalized eigenvector matrix and generalized eigenvalue matrix for the matrix pencil,

Rx and Qx. So the demixing matrix is determined by the generalized eigenvector matrix

of Rx and Qx.

Let us now come to the different assumptions we can impose on the sources and

the corresponding cross statistics matrix Qx. In addition to the independence assumption,

there are basically three types of assumptions you can have on s (t). They are:

Non-Stationary Sources.

Non-White Sources.

Non-Gaussian Sources.

When the sources are non-stationary, the covariance of the observations varies with time t

i.e.

Rx (t) = E[x(t)xH (t)] = AR, (t)AH (2-30)

(2-30) is in the form similar to (2-25). So we can set Qx=Rx (t), for any time t. This Qx

will give the diagonal cross-statistics of (2-25), required for the generalized eigenvalue

equation (2-29). So the demixing matrix, can be identified by simultaneously

diagonalizing multiple covariance matrices (here Rx and Qx) estimated over different

stationary times.

When the sources are non-white, we can use second order statistics in the form of

cross-correlations for different time lags T. The covariance matrix for lag T is given by:

R, (T) = E[x(t)xH (t + T)] = AR, (T)AH (2-31)

Again, (2-31) is of the form given by (2-25). So for any choice of T, the required cross-









statistics matrix Qx=Rx (T). This method of separating the mixtures of independent

signals using time delayed correlations is first studied by Molgedey and Schuster in [17].

The non-Gaussian assumption of the sources is useful when the sources are both

stationary and white. For such sources different t and T do not provide new information

and we have to consider higher order statistics. The 4th order cumulants of the observable

data x (t) expressed in terms of the fourth order moments can be written as:

Cum(x1, x1, x,, x* ) = E[x, x xk x ] -E[x, x ]E[xk x ] -E[x, xk ]E[x x ]E[x x ]E[x xk ]

(2-32)

When the distribution of x is Gaussian, the fourth order cumulant shown above

goes to zero. If the distribution is non-Gaussian, the cumulant goes to zero only when the

distribution of x is composed of independent variables. In [18] a linear combination of

the fourth order cumulants is defined as:

q,j (M) = Cum(x,, x x )lk (2-33)
kJ

Noting that the covariance of x is Rx = E[xxH ] and M= { mIk }, (2-33) becomes,

Qx (M) = E[xHMxxxH RTrace(MR) -E[xxT ]MT E[x'xH ] RxMRx

(2-34)

Replacing M by I, makes Qx sum over all the cumulants given by,

Qx (I) = E[xHxxxH ]- RTrace(R,) -E[xxT ]E[x*xH ]- RR, (2-35)

Observing that x(t)=As(t), we see that

Qx(I) AQ,(AHA)AH (2-36)

where Qs(AHA) is always diagonal for any A. So Qx satisfies the conditions given by (2-

25).









Let us now see how each of these three assumptions can be applied to the fetal

ECG extraction problem. For the non-stationary assumption, the cross-statistics matrix

Qx is computed by considering a window of data of length equal to the period of the

maternal ECG. The covariance matrix is computed using all the data. For the non-white

assumption, the parameter T is chosen empirically so that Qx can be computed to give the

best performance. For the non-Gaussian assumption, there will be no parameters to

choose and Qx is computed as the sum over all the 4th order cumulants.

Table 2-1 shows all the details of the blind source separation using the

Generalized eigenvalue decomposition method. The observable data is represented as a

matrix X of size NxT, where N is the number of sensors (channels) and T is the number

of samples in each channel. In MATLAB, the demixing matrix (W) is calculated as

shown below for all the three assumptions:

[W,D]= eig(R, Q,)











Table 2-1. Summary of procedures for BSS using Generalized Eigenvalue
Decomposition (GED) for fetal ECG extraction
Sources are Matrices on which GED has to be Details
assumed to be carried out
Rx Ox
Non Stationary and XXT E[x(t)xH (t)= t is the number of
decorrelated X- samples over which the
(:, t) t) signal is assumed to be
stationary(chosen to be
120)
Non-White and XXT E[x(t)xH (t + )] = Qx is symmetric and
decorrelated X(:,1: T c) x lag r provides new
information if the
X(:, T+1: T) + sources have distinct
X(:, T +1: T) x autocorrelation. r is set
X(:,1: T to 5 empirically.
Non-Gaussian and XXT E[xHxxH ]- Qx is the sum over 4th
independent RxTrace(Rx) order cumulants.

E[xx. ]E[x*xH]-
RxR,














CHAPTER 3
RESULTS

This chapter discusses and compares the quality of the fetal ECG obtained by

each of the three algorithms explained in the previous chapter viz MeRMaId, Generalized

Eigenvalue Decomposition and the Cauchy Schwartz based quadratic mutual information

minimization method. The algorithms are applied on two different data sets. First to see if

the algorithms work for the particular application of fetal ECG extraction, they are tested

with the normal ECG data of pregnant mother. Then, to see how the algorithms perform

during the uterine contractions of the mother, they are tested with the noisy ECG data of

the mother during the contractions. It has to be noted that all the ICA algorithms suffer

from the problem of scale and permutation i.e. we can never know which output channel

corresponds to the signal of interest (here the fetal ECG). Also we need to come up with a

criterion which measures the quality of the signal of interest. So there arises a need to

make use of some automated algorithms which automatically detect the presence of the

signal of interest as well as assess the quality of it. The results obtained for the data

during contractions are compared qualitatively using a criterion called the trust factor

[19]. This trust factor varies from 0 to 1, the higher value it has the better will be the

quality of the fetal ECG.

The next section tells more about the data collection procedure and the following

sections deal with the results of various algorithms for normal ECG data as well as for the

ECG data during the contractions. Finally the section on the qualitative comparison of the

results using the trust factor concludes the chapter.









Data Collection

The ECG data [20] is collected non-invasively using ten surface electrodes

positioned on the maternal abdomen in a standard arrangement (Figure 3-1). Electrode

position was systematically varied in a preliminary study on 11 patients, until the

following optimal array positioning was identified: 10 electrodes encircling the maternal

abdomen, with reference electrodes located centrally and on the right leg. This standard

position is slightly modified for every patient due to the presence of other monitoring

equipment placed on the maternal abdomen (Tocodynamometer and Ultrasonic belts).

Four of the electrodes also collect EHG signals.













EH6 lead 2 -
Ground




Figure 3-1: Position of the electrodes on the pregnant woman

The recorded signals are fed to an 8-channel high resolution (gain of 4000), low-

noise unipolar amplifier specifically designed for FECG signals. All eight signals were

measured with respect to a reference electrode. The amplifier also uses a driven right leg

(DRL) circuitry to reduce common mode noise between the patient and the amplifier

common. The amplifier 3dB bandwidth is 0.1 Hz and 100 Hz, with a 60 Hz notch. The









amplifier has a variable gain, but here the gain is set to 6,500. The data are then

transferred to a PC via an A/D card which has a sampling frequency of 200Hz and

resolution of 16 bits.

Performance of the Algorithms on Normal ECG Data

MeRMaId Algorithm

The MeRMaId algorithm is first applied to a normal ECG data set collected from

a pregnant mother. The ECG is generally measured by placing eight electrodes on various

places of the mother's abdomen and thorax. So the data will be eight dimensional as

shown in figure 3-2. For the present research, all eight channels have been considered. In

each channel, 10,000 samples of data are considered. Since the sampling rate is 200Hz,

this corresponds to 50 seconds of the ECG monitoring. Preprocessing is done by passing

the data through a second order FIR filter which has zeros at DC and near Nyquist

frequency. This is done to remove the DC bias present in the signal as well as the high

frequency noise. The stochastic information gradient (SIG) version [21] of the algorithm

has been used. The SIG can be used to modify the MeRMaId criterion such that the

complexity is reduced to O(L) from O(L2). The information potential given in (2-12) can

be represented as:


Va (Y)= fy(y)dy=Ey[fy- (y)] (3-1)
-O0

Dropping the expectation and stochastically approximating the value of the information

potential with the instantaneous value of its argument, we get

Vu, () f" (Yk) (3-2)

So the Renyi's Quadratic marginal entropy in (2-12) reduces to:









k-1
HR2,k (Yd) = -log1 G(yd(k)- yd(j),2a2) (3-3)
Lj=k-L

The various parameters for this algorithm are set like this:

alpha = step size is set to 0.01

L = window size is set to 200

rep = number of repetitions is set to 1(since we are using SIG)

stp = order of difference equation (1 DAstp) is set to 1

sig = standard deviation for Gaussian distribution (used for Parzen
windows) is set to 0.25


The outputs (whose Renyi's Mutual Information has been minimized) obtained

for this clean data set are shown in figure 3-3. It can be clearly seen from this figure, that

the mother ECG and the fetal ECG signals are well separated. In this figure, the output

channels 1 and 2 represent the maternal ECG signals, channel 3 represents fetal ECG

signal and the rest of the channels represent the noise.














x 104
5




o n
0
-5 104
0
5 4



-2 104 .
2( 200





-l 1U 290
0


-24
0



2 0


-25 10 200
0





-2 104
0
-2
0 200


Figure 3-2: Eight channels of normal ECG data. Only 2000 samples of the ECG data are

shown in the figure.


8Pn 1000 12Pn 14O0 1R6n 1Ann 7000

800 1000 1200 1400 1600 1800 2000





900 1000 1200 1400 16100 18100 000
i i 1 i ~





I0 1000 120 1400 1RO 10 2000



800 1000 1200 1400 1600 1800 2000


0 1000 1200 1400 160 18 2000

800 1000 1200 1400 1600 1800 2000


-












600
6o0







6o0







6o0



600













MECG
-10 --------


-5 i i i i
10n 200 400 OOn 0n 1000nn 100nn 1400 OOnn 100 000
FECGO ,
-10
50 200 400 600 800 1000 1200 1400 1600 1800 2000
I : : .
5 2o0 490 690o 90 1000 12oo 1400 1o00 10o f o000


50 200 400 600 800 1000 1200 1400 1600 1800 2000

-5

C I I A
50 200 400 600 800 1000 1200 1400 1600 1800 2000


-5
0 200 400 600 800 1000 1200 1400 1600 1800 2000


Figure 3-3: Output signals for the MeRMaId algorithm. The nature of the eight signals is
mentioned to the left.


Cauchy Schwartz based Quadratic Mutual Information

The blind source separation problem is now accomplished using the minimization


of Cauchy Schwartz (CS) based Quadratic Mutual Information (QMI). To make this


algorithm work for the real ECG data, we need to know how to change the kernel size so


that we can get good results. To test if the algorithm separates the sources successfully,


let us first deal with 2 dimensional speech data which are mixed artificially with a known


mixing matrix. The weight matrix, the final value of which will represent the demixing


matrix, is initially chosen as the identity matrix. The kernel size is linearly decreased for


the first 150 iterations and for the next 150 iterations its value (the value at the end of the


150th iteration) is fixed. The step size as well as the momentum learning constant is


chosen as a function of the kernel size, so that we can have larger updates when the











kernel size is larger and smaller updates when the kernel size decreases. The signal to

interference ratio is shown below in figure 3-4. Defining Signal to Interference Ratio


(SIR) as



SIR(i) = 10ogo (max )2 (3-4)
O,0, -(max(O,))2


where 0 = W*A = product of mixing matrix and current estimate of demixing matrix and


Oi represents the ith row of matrix 0.

It can be clearly observed that very high SIR (as high as 50 dB) can be achieved


for this 2 dimensional case. The learning curve which indicates how the cost function


(here the Cauchy Schwartz based Quadratic Mutual Information) varies as the iterations


proceed is shown in figure 3-5.


80

70 -

60

50

E 40
4/Co


30-

20 / /

10- 5


0 50 100 150 200 250 300
Iterations


Figure 3-4: Plot of the signal to interference ratio versus the iterations












0018

0016-

0 014

0012 -

o 001 -

S 0 008

0 006

0 004

0 002

0 5L0 L L ---
0 50 100 150 200 250 300
Iterations


Figure 3-5: Learning curve


Let us now try this algorithm on the normal ECG data. Since estimating the joint


pdf of finite data samples is easy to estimate accurately in lower dimensional space, only


four channels (out of the eight) of the ECG data is considered. The weights are initialized


as the identity matrix as before. The number of iterations on the data is chosen as 500. In


order to make the algorithm escape local minima, kernel annealing (described in chapter


2) is done. For half the number of iterations, kernel annealing is done (kernel size is


gradually decreased linearly from a large value to a predetermined smaller value). For the


next half the number of iterations, the kernel size is fixed. The results for this four


dimensional data are shown in figure 3-6. It can be clearly seen that fetal ECG can be


easily separated and is observed in channel 3 of the output.




















200 400

200 400




200 400


600 800
600 800

I i I


1000 1200


2




-2-
0



0
0.2





-0.2
0
0.5 F


FECG 0C


-0.5
0
5


MECG 0


-5 -
0


200 400 600 800 1000 1200






200 400 600 800 1000 1200


1400 1600


1600 1800


1400 1600 1800






1400 1600 1800


Figure 3-6: Output signals for CS- Based QMI Minimization


Generalized Eigenvalue Decomposition Algorithm



The same data (8 by 10000 samples) is applied as input to this algorithm. All the


three different assumptions (non-stationary, non-white and non-Gaussian) on the data are


tried out. It can be seen from the results shown in figures 3-7, 3-8 and 3-9, that we can


successfully separate the fetal ECG signal and the mother ECG signal from the input


data. The channels representing the signals are shown labeled on the left in these figures.


Let us now come to the parameters chosen for each of the three assumptions. The


stationarity length parameter 't' for the non-stationary assumption case is chosen as 120


samples. The parameter T for the non-white assumption is set to 5. There are no


parameters for the non-Gaussian assumption.


800 1000














Non Stationary


0.1
0
-0.1
0.50 200 400 600 800 1000 1200 1400 1600 1800 2000
0
-0.5
050 200 400 600 800 1000 1200 1400 1600 1800 2000
MECG 0 I
-0.5 5 ---,'-80-
0.50 200 400 600 800 1000 1200 1400 1600 1800 2000
MECG 0
-0.5
10 200 400 600 800 1000 1200 1400 1600 1800 2000
FECG 0
_1
10 200 400 600 800 1000 1200 1400 1600 1800 2000

-1 L L

20 200 400 600 800 1000 1200 1400 1600 1800 2000
0I

10 200 400 600 800 1000 1200 1400 1600 1800 2000
C
-1
0 200 400 600 800 1000 1200 1400 1600 1800 2000





Figure 3-7: 2000 samples of the outputs signals for the Generalized Eigenvalue

Decomposition method using non-stationary Assumption















Non White


10001
0 ,
-1000I
20000


-2000
5000
C,
-5001
20000
FECG C
-20001
16
MECG C0
-1I
50000
MECG 0
-50001
5000


-500
10000
0
1000
0
o


200



200



200


10 200



200



200



200



200


Figure 3-8: 2000 samples of the outputs signals for the Generalized Eigenvalue

Decomposition method using non-white assumption


400 600 800 1000 1200 1400



400 600 800 1000 1200 1400



400 600 800 1000 1200 1400



400 600 800 1000 1200 1400



400 600 800 1000 1200 1400



400 600 800 1000 1200 1400



400 600 800 1000 1200 1400



400 600 800 1000 1200 1400


1600 1800 2000



1600 1800 2000



1600 1800 2000



1600 1800 2000



1600 1800 2000



1600 1800 2000



1600 1800 2000



1600 1800 2000












Non Gaussian


500
0.
-500
20000 200
FECG 0 4
2000


ME





ME(


400 600 800 1000 1200 1400 1600 1800 20


5000 200 400 600 800 1000 1200 1400 1600 1800 2000

-500
50000 200 400 600 800 1000 1200 1400 1600 1800 2000
CG 0
-5000
20000 200 400 600 800 1000 1200 1400 1600 1800 2000
0 ,
-2000 -----100 100 80
1 10 200 400 600 800 1000 1200 1400 1600 1800 2000
CG 0
-1 1 1 1 1 1 1 1 1 1 1 1
1000(0 200 400 600 800 1000 1200 1400 1600 1800 2000
-1000 ,--------------------------------------
-1000
nonn0 200 400 600 800 1000 1200 1400 1600 1800 2000


4,, ,.0 _r I,,,,, i 4,,,, hr. 0 I -" -, ,00




Figure 3-9: 2000 samples of the outputs signals for the Generalized Eigenvalue
Decomposition method using non-gaussian assumption


Performance of the Algorithms on the Data during Contractions


Figure 3-10 shows the nature of the input data during contractions. Due to the


presence of the ElectroHysteroGram (EHG) signal, the ECG data is noisier. We now


attempt to separate the fetal ECG signal from eight channels of such data. The output


signals obtained from the MeRMaId, the three different cases of the generalized


eigenvalue decomposition algorithm are shown in figures 3-11, 3-12, 3-13, 3-14


respectively. It can be visually observed from these plots, that the MeRMaId algorithm


totally fails to extract the fetal ECG. The quality of the extracted fetal ECG is


comparatively better for the Generalized Eigenvalue Decomposition method based on


non-white assumption. We will deal with the comparison more rigorously and


qualitatively in the next section. The Cauchy-Schwartz based Quadratic Mutual











Information minimization method failed to extract the fetal ECG from the 8 dimensional


ECG data during the contractions. The reason is considered to be more due to the


dimensionality of the data rather than due to the nature of the data. This problem with


high dimensionality of the data is not an issue with the MeRMaId algorithm since only


marginal pdf's are estimated in this algorithm (no need to estimate the joint) whereas CS-


QMI has this additional problem of estimating the joint pdf in higher dimensional space.



6000-

4000

20000



-2000


0 0.5 / 1 1.5 2- 2.5 3
S- --x 104

6000--

4000

2000



-2000

-4000
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000




Figure 3-10: One channel of ECG data during uterine contractions. The figure
shown at the bottom zooms on the portion of the signal containing contractions.















MerMaid


10
MECG 0
-10
100 200 400 600 800 1000 1200 1400 1600 1800 2000
MECG 0
-10
50 200 400 600 800 1000 1200 1400 1600 1800 2000
0
-5
50 200 400 600 800 1000 1200 1400 1600 1800 2000
FECG c,,
-5
50 200 400 600 800 1000 1200 1400 1600 1800 2000



50 200 400 600 800 1000 1200 1400 1600 1800 2000


-5
-51
50 200 400 600 800 1000 1200 1400 1600 1800 2000

50 200 400 600 800 1000 1200 1400 1600 1800 2000



0 200 400 600 800 1000 1200 1400 1600 1800 2000
-5Il


Figure 3-11: Output signals for the MeRMaId algorithm














Non Stationary Assumption


0.5
FECG 0
-0.5 L L L _-
050 200 400 600 800 1000 1200 1400 1600 1800 2000

-0.5
0.50 200 400 600 800 1000 1200 1400 1600 1800 2000

-0.5
0.50 200 400 600 800 1000 1200 1400 1600 1800 2000

-0.5
0.50 200 400 600 800 1000 1200 1400 1600 1800 2000

-0.5
0.50 200 400 600 800 1000 1200 1400 1600 1800 2000
0
-05
"0 200 400 600 800 1000 1200 1400 1600 1800 2000
MECG 0
-5
100 200 400 600 800 1000 1200 1400 1600 1800 2000
MECG 0
10
0 200 400 600 800 1000 1200 1400 1600 1800 2000





Figure 3-12: 2000 samples of the outputs signals for the Generalized Eigenvalue

Decomposition method using non-stationary assumption














Non White Assumption


500

-500
5000 200 400 600 800 1000 1200 1400 1600 1800 2000

-500
10000 200 400 600 800 1000 1200 1400 1600 1800 2000
FECG 0 ,
-1000 j---------"-'"
S10J 200 400 600 800 1000 1200 1400 1600 1800 2000

MECG 0 -
-1
10000 200 400 600 800 1000 1200 1400 1600 1800 2000
MECG 0
-1000
5000 200 400 600 800 1000 1200 1400 1600 1800 2000

-500
500(0 200 400 600 800 1000 1200 1400 1600 1800 2000

-500
5000 200 400 600 800 1000 1200 1400 1600 1800 2000

-500
0 200 400 600 800 1000 1200 1400 1600 1800 2000





Figure 3-13: 2000 samples of the outputs signals for the Generalized Eigenvalue
Decomposition method using non-white assumption













Non Gaussian Assumption


5001

-500
5000 200 400
C' *
-5001
10000 200 400
C' .
-1000
1 10 200 400

MECG 0
2 10 200 400

MECG 0
-2
500o0 200 400
0
-500
50 200 400

-5001
5000 200 400
FECG '
-5001
0 200 400


600 800 1000


600 800 1000


1200


1200


1400 1600


1400 1600


1800


1800


600 800 1000 1200 1400 1600 1800 2000


600 800 1000 1200 1400 1600 1800 2000


600 800 1000 1200 1400 1600 1800 2000


600


600


600


1000


1000


1000


1200


1200


1200


1400 1600


1400 1600


1400 1600


1800


1800


1800


Figure 3-14: 2000 samples of the outputs signals for the Generalized Eigenvalue
Decomposition method using non-gaussian assumption


Comparison of the Performance of the Algorithms


In order to compare the performance of these algorithms, a criterion called trust


factor [19] is defined which measures the quality of fetal ECG. This is based on the Pan-


Tompkins online QRS detection algorithm [22]. The output signals from the ICA


algorithms are first passed through a band pass filter in order to remove the interfering


noise. The outputs of this filter are differentiated and squared. This is followed by an


integration stage realized using a moving average filter. Then thresholds are set to locate


the peaks, which essentially gives the beat to beat heart rate. Different thresholds are set


to determine maternal heartbeat and fetal heartbeat. The quality of the fetal ECG is


judged based on the number of false positives (peaks observed when none are there


actually) and on the number of false negatives (no peaks observed when there are actual


2000


2000


2000









peaks). This is determined by measured the interval between any two consecutive peaks.

If this interval is less than 70% of the 5 previous RR intervals average, then there is a

false positive. If this interval is more than 130% of the 5 previous RR intervals average,

then there is a false negative. Based on these false positives and false negatives, a

criterion is developed, called the Trust Factor, to judge the quality of the fetal ECG.

The Trust Factor goes from 0 to 1 and uses several characteristics of ECG signals

including:

The quasi periodicity of the signal

The sparseness of the signal (or the ECG-look) calculated with the number
of points below a certain threshold or the kurtosis of the signal
*
The level of noise in the signal (which is calculated by two different
methods: an estimation of the false negatives and false positives, and a
signal to noise ratio in the autocorrelation function)
*
The location of the QRS peaks

The performance of the algorithms for normal ECG data is compared using the

Trust Factor. A window of data containing 8 channels of 10000 samples is considered for

the algorithms MeRMaId, Generalized Eigenvalue Decomposition (GED) based on Non

Stationary (NS) assumption, Generalized Eigenvalue Decomposition (GED) based on

Non White (NW) assumption and Generalized Eigenvalue Decomposition (GED) based

on Non Gaussian (NG) assumption. The data from the same window by of size 4 by 2000

is considered for the Cauchy Schwartz (CS) based Quadratic Mutual Information (QMI)

algorithm. The values for the Trust Factor for each algorithm are shown in table 3-1.

To compare the performance of these algorithms during the contractions, five

windows each containing 10000 samples of the eight dimensional data is considered and

each algorithm is applied to it. The resulting value of the trust factor is shown in the table









3-2. The results for CS-QMI are not presented for this data set since the algorithm failed

to extract the fetal ECG (reasons mentioned earlier in the chapter) while dealing with this

dataset.

Table 3-1. Comparison of performance of the BSS algorithms for normal ECG
Window
Number Trust Factor

MeRMaId GED NS GED NW GED NG CS-QMI

1 0.7747 0.7640 0.7115 0.7983 0.4859



Table 3-2. Comparison of performance of the BSS algorithms for ECG data during
contractions

Window Number Trust Factor

MerMaid GED NS GED NW GED NG

1 0.1975 0.2180 0.3823 0.3002


2 0.3996 0.5036 0.5261 0.4692


3 0.6375 0.4806 0.5690 0.5830


4 0.7306 0.7162 0.6521 0.5424


5 0.6752 0.7214 0.6348 0.6072


Mean 0.5281 0.5280 0.5528 0.5004














CHAPTER 4
CONCLUSIONS AND FUTURE WORK

Conclusions

All the three algorithms BSS using MeRMaId, BSS using Generalized Eigenvalue

Decomposition (GED) BSS using Cauchy Schwartz (CS) based Quadratic Mutual

Information(QMI) are used to extract the fetal ECG from two different data sets :normal

ECG recordings and ECG recordings during the uterine contractions of a pregnant

woman. From the results presented in chapter 3 the following conclusions can be drawn:

1. MeRMaId

The MeRMaId algorithm extracts the fetal ECG from the normal ECG data and

the quality of the extracted fetal ECG is quite good. However, this algorithm fails to give

good quality fetal ECG when dealing with the ECG data during the contractions. The

reason for this poor performance can be attributed to the spatial pre-whitening step

performed on the observations, which worsens the already poor SNR.

2. GED

The GED algorithm, based on all the three assumptions on the data, non-

stationary, non-white, non-Gaussian, gives a high quality fetal ECG from the normal

ECG data. On the data during the contractions, the non- white assumption gives the best

performance in terms of the quality of fetal ECG as measured by the criterion given by

[20]. The non-stationary assumption gives results slightly superior to that of the

MeRMaId while the non-Gaussian assumption gives results slightly worse than the

MeRMaId algorithm.









3. CS QMI

This algorithm gives very promising results for lower dimensional data as

illustrated by the blind source separation of a 2 dimensional speech data which is

artificially mixed. But the algorithm suffers in performance as the dimensionality of the

data is increased. To test the performance on the normal ECG data, only 4 (out of 8)

channels are considered. The algorithm gives a good quality fetal ECG using these 4

channels only. But the data during the contractions, being noisier, inherently has more

independent sources. So there arises the need to use all the 8 channels which makes the

algorithm give poor results (no fetal ECG is observed).

Scope for Future Work

There are a couple of ideas, which researchers have successfully used to solve the

blind source separation problem. These methods are particularly appealing for the ECG

data which we have dealt with.

Zibulevsky and Pearlmutter [23] exploited the property of the sources having a

sparse representation in a signal dictionary for blind source separation and obtained very

promising results. The dictionary may consist of wavelets, wavelet packets or coefficients

in any other domain where they are sparse. The ECG signals can be considered to be

having a sparse distribution in time since the active portions in the signal last only for a

small amount of time. But the presence of noise (especially during the contractions)

makes this assumption of sparse sources to be weak. But if we can have a denoising

algorithm which improves the SNR significantly, then we can expect a superior

performance by this algorithm for this application.

Least dependent component based on Mutual Information (MILCA) proposed by

Stogbauer et al [24] is very interesting in the sense that they take into account the time









structure of the signal while doing a blind source separation. In this work, they propose to

use a Mutual Information (MI) estimator based on k-nearest neighbor statistics [23].

Using this estimate of MI, they find the least dependent components in a linearly mixed

signal. The fact that we are finding only the least dependent components instead of

independent components is very useful for the problem of fetal ECG extraction because

the fetal heartbeats and mother heartbeats are not entirely independent. By making use of

the time structure and higher order statistics we can obtain optimal results in general. By

delay embedding the observable signals (here non-invasive measurements of a pregnant

mother), promising results have been obtained. This method of minimizing the mutual

information of the delay embedded signals will give outputs which are least dependent. It

would be really interesting to apply this method to the ECG recordings during

contractions and minimize the k-nearest neighbor estimate of MI (if not Renyi's MI).















LIST OF REFERENCES


1. Bernard Widrow, Samuel D Stearns: Adaptive Signal Processing, Prentice Hall
Inc., Upper Saddle River, NJ, 1985.

2. G Camps, M Martinez, E Soria: Fetal ECG Extraction using an FIR Neural
Network, Computers in Cardiology, 23-26 September 2001.

3. F Mochimaru, Y Fujimoto: Detecting the Fetal Electrocardiogram by Wavelet
Theory-Based Methods, Progress in Biomedical Research, Vol.7, No.2,
September 2002.

4. S Mallat, W L Hwang: Singularity Detection and Processing with Wavelets, IEEE
Transactions on Information Theory, Vol. 38, Issue. 2, pp. 617-643, March 1992.

5. V Vigneron, A Paraschiv-Ionescu, A Azancot, 0 Sibony, C Jutten: Fetal
Electrocardiogram Extraction Based On Non-Stationary ICA And Wavelet
Denoising, Proceedings Seventh International Symposium on Signal Processing
and Its Applications, Vol. 2, pp. 69-72 1-4, July 2003.

6. D T Pham, J F Cardoso: Blind Separation of Instantaneous Mixture of Non-
Stationary Sources, IEEE Transactions on Signal Processing, 49(9), pp. 1837-
1848, 2001.

7. K S Tang, K F Man, S Kwong, Q He: Genetic Algorithms and their Applications,
IEEE Signal Processing Magazine, Vol. 13, Issue. 6, pp. 22-37, November 1996.

8. S Horner, W Holls, P B Crilly: Non-invasive Fetal Electrocardiograph
Enhancement, Proceedings of Computers in Cardiology, pp. 163-166, 11-14
October 1992.

9. A Kam, A Cohen: Detection of Fetal ECG With IIR Adaptive Filtering and
Genetic Algorithms, IEEE International Conference on Acoustics, Speech, and
Signal Processing, Vol. 4, Pages.2335 2338, 15-19 March 1999.

10. Allan Kardec Barros, Andrzej Cichocki: Extraction of Specific Signals with
Temporal Structure, Neural Computation, Vol. 13, Issue. 9, September 2001.

11. Kenneth E Hild II, Deniz Erdogmus, Jose Principe: Blind Source Separation
Using Renyi's Mutual Information, IEEE Signal Processing Letters, Vol. 8, No. 6,
June 2001.









12. Dongxin Xu, Jose C Principe, John Fisher III, Hsiao-Chun Wu: A Novel Measure
for Independent Component Analysis (ICA), ICASSP, Vol. II, pp. 1161-1164,
1998.

13. Lucas Parra, Paul Sajda: Blind Source Separation via Generalized Eigenvalue
Decomposition, Journal of Machine Learning Research 4, pp. 1261-1269, 2003.

14. A. Renyi: Probability Theory, Amsterdam, The Netherlands, North Holland,
1970.

15. Jose C Principe, Dongxin Xu: Information Theoretic Learning using Renyi's
Quadratic Entorpy, International Conf. on ICA and Signal Separation, pp. 407-
412, August 1999.

16. Jose C Principe, Dongxin Xu, John W Fisher III: Information Theoretic Learning,
Book Chapter in Unsupervised Adaptive Filtering, John Wiley & Sons, Inc., New
York, NY, 2000.

17. L. Molgedey, H.G. Schuster: Separation of a Mixture of Independent Signals
Using Time Delay Correlations, Physics. Review. Letters. 72, Issue. 23, pp. 3634-
3637, June 1994.

18. J F Cardoso, A. Souloumiac: Blind Beamforming for Non-Gaussian Signals, IEE
Proceedings, Vol. 140, No. 6, December 1993.

19. Dorothee E Marossero, Deniz Erdogmus, Neil Euliano, Jose C Principe, Kenneth
E Hild II: Independent Components Analysis For Fetal Electrocardiogram
Extraction: A Case For The Data Efficient MERMAID Algorithm, Proceedings of
NNSP'03, pp.399-408, Toulouse, France, September 2003.

20. T Y Euliano, D E Marossero N R Euliano B Ingram, K Andersen, R K
Edwards: Non-invasive Fetal ECG: Method Refinement and Pilot Data,
Anesthesia and Analgesia, in press.

21. Kenneth E Hild II, Deniz Erdogmus, Jose C Principe: On-line Minimum Mutual
Information Method for Time Varying Blind Source Separation, International
Conference on ICA and Signal Separation, pp. 126-131, San Diego CA, December
2001.

22. J Pan, W J Tompkins : A Real Time QRS Detection Algorithm, IEEE
Transactions on Biomedical Engineering, Vol. 32, No. 3, pp. 837-843,1985.

23. Michael Zibulevsky, Barak A Pearlmutter: Blind Source Separation by Sparse
Decomposition, Neural Computation, Vol. 13, Issue. 4, pp. 863-882, April 2001.

24. Harald Stogbauer, Alexander Kraskov, Sergey A Astakhov, Peter Grassberger:
Least Dependent Component Analysis Based on Mutual Information, DOI:
physics/0405044, arXiv, 2004.






47


25. A Kraskov, H Stogbauer, P Grassberger: Estimating Mutual Information, Physics
Review E, 2004.















BIOGRAPHICAL SKETCH

Hemanth Peddaneni received his bachelor's degree in electronics and

communication engineering, from Sri Venkateswara University, Tirupati, India, in 2002.

He has been a Young Engineering Fellow, awarded by the Indian Institute of Science,

Bangalore, India. He is now pursuing his master's degree in electrical and computer

engineering at the University of Florida. His research interests include neural networks

for signal processing, adaptive signal processing, wavelet methods for time series

analysis, digital filter design/implementation and digital image processing.