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Real-time landmine detection with ground-penetrating radar using discriminative and adaptive hidden Markov models
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Permanent Link: http://ufdc.ufl.edu/AA00008932/00001
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Title: Real-time landmine detection with ground-penetrating radar using discriminative and adaptive hidden Markov models
Series Title: EURASIP Journal on Applied Signal Processing
Physical Description: Archival
Language: English
Creator: Frigui, Hichem
Ho, K. C.
Gader, Paul
Publisher: BioMed Central
Hindawi Publishing Corporation
Publication Date: 2005
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Abstract: We propose a real-time software system for landmine detection using ground-penetrating radar (GPR). The system includes an efficient and adaptive preprocessing component; a hidden Markov model- (HMM-) based detector; a corrective training component; and an incremental update of the background model. The preprocessing is based on frequency-domain processing and performs ground-level alignment and background removal. The HMM detector is an improvement of a previously proposed system (baseline). It includes additional pre- and postprocessing steps to improve the time efficiency and enable real-time application. The corrective training component is used to adjust the initialmodel parameters to minimize the number of misclassification sequences. This component could be used offline, or online through feedback to adapt an initial model to specific sites and environments. The background update component adjusts the parameters of the background model to adapt it to each lane during testing. The proposed software system is applied to data acquired from three outdoor test sites at different geographic locations, using a state-of-the-art array GPR prototype. The first collection was used as training, and the other two (contain data from more than 1200 m2 of simulated dirt and gravel roads) for testing. Our results indicate that, on average, the corrective training can improve the performance by about 10% for each site. For individual lanes, the performance gain can reach 50%.
General Note: Publication of this article was funded in part by the University of Florida Open-Access publishing Fund. In addition, requestors receiving funding through the UFOAP project are expected to submit a post-review, final draft of the article to UF's institutional repository, IR@UF, (www.uflib.ufl.edu/ufir) at the time of funding. The Institutional Repository at the University of Florida (IR@UF) is the digital archive for the intellectual output of the University of Florida community, with research, news, outreach and educational materials
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Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution.
Resource Identifier: doi - 1687-6180-2005-419248
System ID: AA00008932:00001

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EURASIPJournalonAppliedSignalProcessing2005:12,1867c 2005HindawiPublishingCorporationReal-TimeLandmineDetectionwithGround-PenetratingRadarUsingDiscriminativeandAdaptiveHiddenMarkovModelsHichemFriguiDepartmentofComputerEngineeringandComputerScience,UniversityofLouisville,Louisville,KY40292,USAEmail:h.frigui@louisville.eduK.C.HoDepartmentofElectricalandComputerEngineering,UniversityofMissouri-Columbia,Columbia,MO65211,USAEmail:hod@missouri.eduPaulGaderDepartmentofComputerandInformationScienceandEngineering,UniversityofFlorida,Gainesville,FL32611,USAEmail:pgader@cise.u.eduReceived25October2004;Revised3March2005;RecommendedforPublicationbyFulvioGiniWeproposeareal-timesoftwaresystemforlandminedetectionusingground-penetratingradarGPR).Thesystemincludesane cientandadaptivepreprocessingcomponent;ahiddenMarkovmodel-(HMM-)baseddetector;acorrectivetrainingcom-ponent;andanincrementalupdateofthebackgroundmodel.Thepreprocessingisbasedonfrequency-domainprocessingandperformsground-levelalignmentandbackgroundremoval.TheHMMdetectorisanimprovementofapreviouslyproposedsystem(baseline).Itincludesadditionalpre-andpostprocessingstepstoimprovethetimee ciencyandenablereal-timeapplica-tion.Thecorrectivetrainingcomponentisusedtoadjusttheinitialmodelparameterstominimizethenumberofmisclassicationsequences.Thiscomponentcouldbeusedo ine,oronlinethroughfeedbacktoadaptaninitialmodeltospecicsitesandenvi-ronments.Thebackgroundupdatecomponentadjuststheparametersofthebackgroundmodeltoadaptittoeachlaneduringtesting.Theproposedsoftwaresystemisappliedtodataacquiredfromthreeoutdoortestsitesatdi erentgeographiclocations,usingastate-of-the-artarrayGPRprototype.Therstcollectionwasusedastraining,andtheothertwocontaindatafrommorethan1200m2 ofsimulateddirtandgravelroads)fortesting.Ourresultsindicatethat,onaverage,thecorrectivetrainingcanimprovetheperformancebyabout10%foreachsite.Forindividuallanes,theperformancegaincanreach50%.Keywordsandphrases:landminedetection,hiddenMarkovmodels,correctivetraining,adaptivepreprocessing.1.INTRODUCTIONDetectionandremovaloflandminesisaseriousproblemaf-fectingciviliansandsoldiersworldwide.Itisestimatedthatmorethan100millionlandminesareburiedinmorethan80countriesaroundtheworld,andthat26000people,mostlycivilians,ayearareeitherkilledormaimedbyalandmine[ 1 2 ].Thedetectionproblemiscompoundedbythelargevarietyoflandminetypes,di eringsoilconditions,temper-atureandweatherconditions,andvaryingterrain,tonameafew.Detectionandremovaloflandminesisthereforeasignif-icantproblem,andhasattractedseveralresearchersinrecentyears.Onechallengeinlandminedetectionliesinplasticorlowmetalminesthatcannotoraredi culttodetectbytra-ditionalmetaldetectors.Varietiesofsensorshavebeenproposedorareunderin-vestigationforlandminedetection.Theresearchproblemforsensordataanalysisistodeterminehowwellsignaturesoflandminescanbecharacterizedanddistinguishedfromotherobjectsunderthegroundusingreturnsfromoneormoresensors.Ground-penetratingradarGPR)o ersthepromiseofdetectinglandmineswithlittleornometalcon-tent.Unfortunately,landminedetectionviaGPRhasbeenadi cultproblem[3 4 5 ].Althoughsystemscanachievehighdetectionrates,theyhavedonesoattheexpenseofhighfalse-alarmrates.Thekeychallengetominedetec-tiontechnologyliesinachievingahighrateofminedetec-tionwhilemaintaininglowleveloffalsealarms.Theper-formanceofaminedetectionsystemisthereforecommonlymeasuredbyareceiveroperatingcharacteristicsROC)curve

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1868EURASIPJournalonAppliedSignalProcessing thatjointlyspeciesrateofminedetectionandleveloffalsealarm.Automateddetectionalgorithmscangenerallybebro-kendownintofourphases:preprocessing,featureextrac-tion,condenceassignment,anddecision-making.Pre-processingalgorithmsperformtaskssuchasnormalizationofthedata,correctionsforvariationsinheightandspeed,removalofstationarye ectsduetothesystemresponse,andsoforth.MethodsthathavebeenusedtoperformthistaskincludewaveletsandKalmanlters[6 7 ],subspacemeth-odsandmatchingtopolynomials[8 ],andsubtractingopti-mallyshiftedandscaledreferencevectors[9 ].Featureextrac-tionalgorithmsreducethepreprocessedrawdatatoformalower-dimensional,salientsetofmeasuresthatrepresentthedata.Principalcomponent(PC)transformsareacom-montooltoachievethistask[10 11 ].Otherfeatureanaly-sisapproachesincludewavelets[6 ],imageprocessingmeth-odsofderivativefeatureextraction[12 ],curveanalysisusingHoughandRadontransforms[13 ],aswellasmodel-basedmethods[14 ].CondenceassignmentalgorithmscanusemethodssuchasBayesian[13 ],hiddenMarkovmodels[12 ], fuzzylogic[15 16 ],rulesandorderstatistics[17 ],neuralnetworks,ornearest-neighborclassiers[11 18 ],toassignacondencethatamineispresentatapoint.Decision-makingalgorithmsoftenpostprocessthedatatoremovespuriousre-sponsesanduseasetofcondencevaluesproducedbythecondenceassignmentalgorithmtomakeanalmine/no-minedecision.In[12 ],hiddenMarkovmodelingwasproposedforde-tectingbothmetalandnonmetalminetypesusingdatacollectedbyamoving-vehicle-mountedGPRsystem.This(baseline)systemusesbothcontinuousanddiscreteHMMs,andhasprovedthatHMMtechniquesarefeasibleandef-fectiveforlandminedetection.Incomparisonwithenergy-basedmethodsandfuzzygradient-baseddetector,theHMMtechniqueperformedsignicantlybetterthantheformer,andachievedcomparableperformancetothelatter[12 ].ThebaselinediscreteHMMwastrainedbyconventionalmethodsofvectorquantizationandtheBaum-Welchalgorithm.ForthebaselinecontinuousHMM,theparameterswereinitial-izedusingclusteringmethodsandlearnedusingtheBaum-Welchalgorithm.TheperformanceofthecontinuousHMMwasslightlybetterthanthediscreteHMM,andthefusionofthetworesultedinabetterperformancethanthoseoftheindividualdetectors.In[19 ],minimumclassicationerror(MCE)trainingwasproposedtoimprovetheperformanceofthediscretebaselineHMM.Aftertheinitialtraining,thisalgorithmusesasequentialgeneralizedprobabilisticdescentalgorithmthatminimizesanempiricallossfunctiontoestimatethemine/backgroundmodelparameters.Anevolutionaryalgo-rithm,basedonnessscoreofclassicationaccuracy,wasusedtogenerateandselectcodebooks.TheMCE-baseddiscreteHMMachievedasignicantperformanceimprove-mentoverthebaselinesystem.Inthispaper,weproposeandevaluateacompletereal-timesoftwaresystemforlandminedetectionusingGPR.ThedetectorisbasedoncontinuousHMM,andisanimprovedversionofthebaselinesystemproposedin[12 ].First,wepro-poseadi erentpreprocessingtechniquebasedonfrequency-domainprocessingtoperformground-levelalignmentandbackgroundremoval.Thispreprocessingapproachisdi er-entfromtheoneusedinthebaselinedetectorasthetwosystemsweredevelopedfordi erentGPRprototypes,andtheproposedsystemwasdesignedtooperateinareal-timemode.Second,pre-andpostprocessingstepsofthesequenceobservationswereaddedtoimprovethetimee ciencyofthedetectorandenablereal-timeapplication.Third,anim-provedmodeltrainingapproachisproposed.Theparam-etersofthebaselinesystemwerelearnedusingtheBaum-Welchalgorithm.Thisstandardapproachdoesnotguaran-teeminimizationoftheclassicationerrorrate,andcannotbeusedinanonlinemodetoadaptthemodelparameterstodi erentgeographicalsitesandenvironments.Theproposedsystemusesaheuristiccorrectivetrainingproceduretoad-justtheinitialparameterstominimizethenumberofmis-classicationsequences.Ourapproachisbasedontheopti-maldiscriminativetraining(ODTproposedbyMizutaandNakajima[20 ].Thistrainingcouldbeusedo ine,usingasignaturelibrary,toadjusttheparametersofagenericmodel.Itcouldalsobeusedinareal-worldoperationalmode,us-ingfeedbackonwhichmeasurementsareminesandfalsealarmsoncetheyaredug,toadapttheinitialmodeltospe-cicsitesandenvironments.Fourth,weproposeadynamicbackgroundmodelthatcontinuouslyadjustsitsparameterstoadaptittothedi erentlanesduringtesting.Theproposedsoftwaresystemisappliedtodataacquiredfromseveralout-doortestsites,usingastate-of-the-artarrayGPRprototype.Therestofthepaperisorganizedasfollows.InSection2, weproviderelatedbackgroundonHMM,anddi erenttrainingmethods.InSection3,wegiveanoverviewoftheGPRdata.InSection4,wedescribethedi erentcomponentsoftheproposedsystem.InSection5,theexperimentaldata,trainingprocedures,andresultsarediscussedandsumma-rized.ConcludingremarksaregiveninSection6. 2.BACKGROUND2.1.HiddenMarkovmodelsAnHMMisamodelofadoublystochasticprocessthatpro-ducesasequenceofrandomobservationvectorsatdiscretetimesaccordingtoanunderlyingMarkovchain.Ateachob-servationtime,theMarkovchainmaybeinoneofN s states{ s 1 ... s N } and,giventhatthechainisinacertainstate,thereareprobabilitiesofmovingtootherstates.Theseprob-abilitiesarecalledthetransitionprobabilities.AnHMMischaracterizedbythreesetsofprobabilitydensityfunctions,thetransitionprobabilitiesA ),thestateprobabilitydensityfunctionsB ),andtheinitialprobabilities ). LetT bethelengthoftheobservationsequencei.e.,numberoftimesteps),letO ={ O 1 ... O T } betheobserva-tionsequence,andletQ ={ q 1 ... q T } bethestatesequence.Thecompactnotation = A B 1

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1869 isgenerallyusedtoindicatethecompleteparametersetoftheHMMmodel.In1 ), A = [ a ij ]isthestatetransitionprobabilitymatrix,wherea ij = Prq t = j | q t 1 = i )fori j = 1, ... N s ; ={ i } ,where i = Prq 1 = s i aretheini-tialstateprobabilities;andB ={ b i O t ), i = 1, ... N } ,whereb i O t = PrO t | q t = i isthesetofobservationprobabilitydistributioninstatei AnHMMiscalledcontinuousiftheobservationprob-abilitydensityfunctionsarecontinuousanddiscreteiftheobservationprobabilitydensityfunctionsarediscrete.InthecaseofthediscreteHMM,theobservationvectorsarecommonlyvectorquantizedintoanitesetofsymbols,{ v 1 v 2 ... v M } ,calledthecodebook.Eachstateisrepre-sentedbyadiscreteprobabilitydensityfunctionandeachsymbolhasaprobabilityofoccurringgiventhatthesystemisinagivenstate.Inotherwords,B becomesasimplesetofedprobabilitiesforeachclass,thatis,b i O t = b i k = Prv k | q t = i ),wherev k isthesymbolofthenearestcodebookof O t .InthecontinuousHMM,b i O t saredenedbyamix-tureofsomeparametricprobabilitydensityfunctions.ThemostcommonparametricpdfusedincontinuousHMMisthemixtureGaussiandensity:b i O t = M i m = 1 c im b im O t i = 1, ... N ,(2whereM i isthenumberofcomponentsinstatei c im isthemixturecoe cientforthem thmixturecomponentinstatei ,andsatisestheconstraintsc im 0,and M i m = 1 c im = 1, for i = 1, ... N ,andb im O t )isaK -dimensionalmultivariateGaussiandensitywithmean im andcovariancematrixC im GiventheformofthehiddenMarkovmodeldenedin 1 ),Rabiner[21 ]denesthreekeyproblemsofinterestthatmustbesolvedforthemodeltobeusefulinreal-worldap-plications:i)theclassicationproblem,ii)theproblemofndinganoptimalstatesequence,and(iii)theproblemofestimatingthemodelparameters.Theclassicationprob-leminvolvescomputingtheprobabilityofanobservationse-quence{ O ={ O 1 ... O T }} givenamodel ,thatis,PrO | ). Bayesianmethodscanbeusedtoobtaintheprobabilityofthemodelgiventheobservation.Thisprobabilitycanbecom-putedwithO TN 2 computations.Inmostapplications,itoftenturnsoutthatcomputinganoptimalstatesequenceismoreusefulthanPr(O | ).Thereareseveralpossiblewaysofndinganoptimalstatesequenceassociatedwiththegivenobservationsequence,dependingonthedenitionoftheop-timalstatesequence,thatis,thereareseveralpossibleopti-malitycriteria.OnethatisparticularlyusefulistomaximizePrO Q | overallpossiblestatesequencesQ .TheViterbial-gorithm[22 ]isane cient,formaltechniqueforndingthismaximumstatesequenceandassociateprobability.Thethirdproblemisthetrainingproblem:Howdoesoneestimatetheparametersofthemodel?Theproblemisdi cultbecausethereareseverallevelsofestimationrequiredinanHMM.Firstofall,thestatesthemselvesmustbeestimated.Thenthemodelparameters = A B needtobeestimated.InthediscreteHMM,rstthecodebookisdetermined,usu-allyusingtheK-means[21 ],orothervectorquantizational-gorithms.ThentheparametersA B areestimateditera-tivelyusingtheBaum-Welchalgorithm[23 ].Inthecontin-uousHMM,andforthecaseofGaussianmixturedensityfunctions,themixturecomponentparameters, im C im c im arerstinitializedusuallybyclusteringthetrainingdata),andthenthecontinuousversionofBaum-WelchisusedtolearnA B ). 2.2.HMMtrainingforminimizingclassicationerrorThestandardapproachtoestimatetheHMMparametersistousetheexpectation-maximization(EM)algorithm[ 24 ],alsoknownastheforward-backwardorBaum-Welch(BWalgorithm[23 ]inthiscontext,tondthemaximum-likelihood(ML)estimator.Unfortunately,MLtrainingdoesnotguaranteeminimizationoftheclassicationerrorrate.Moreover,assumptionssuchasindependentobservationsorstatetransitionprobabilitiesbeingdependentonlyononepreviousstatemaynotbevalid,andmayresultinasub-optimalperformance.Toalleviatetheseproblems,severalal-ternativetrainingalgorithmshavebeenusedmainlyintheareaofspeechrecognition.Thesemethodscanberoughlydividedintothreecategories:maximummutualinformation(MMI)training,minimumclassicationerror(MCE)train-ing,andcorrectivetraining.InMMItraining,theHMMpa-rametersareestimatedbymaximizingthemutualinforma-tionbetweenanobservationsequenceandthecorrespond-ingsequenceofclasslabels.FortheimplementationofMMI,thereisnoe cientandrobustprocedurethatisguaranteedtoconvergetoanoptimalsolution.In[25 26 ],theobjec-tivefunctionisoptimizedusinggradientsearchtechniqueswithprojectiononconstraints.InMCEtraining,theHMMparametersareestimatedbyformulatingalossfunctionthatincorporatestheclassicationerrorrateoverasetoftrainingdata[27 28 ].Theempiricallossfunctionisminimizedusingageneralizedprobabilisticdescentalgorithm.UnlikeMMIandMCEtrainings,correctivetrainingismotivatedbyintuitionratherthantheoreticaloptimization.ItwasrstintroducedbyBahletal.[29 ]forthediscreteHMM.Asimilarapproach,calledoptimaldiscriminativetraining(ODTwasproposedbyMizutaandNakajima[20 ] forthecontinuousHMM.Inthisapproach,aninitialmodelisusedtoclassifythetrainingsamples,andtheparametersareadjustedwhenanerrorisobservedtoavoidrepeatingthemisclassication.3.GPRDATA3.1.GPRsensorTheGPRsensorsystemismountedunderneathavehicletoprovideathree-meterdetectionswath[30 ].Whenthevehi-clemoves,theGPRtransmitantennasendsoutpulsesthatpenetratetothegroundandthereceiveantennacapturesthereturnedsignalinordertofacilitatethedetectionofland-mine.

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1870EURASIPJournalonAppliedSignalProcessing RxRxRxRxRxRxRxRxRxTxTxTxTxTxTxTxTxTxModule1Module23metersModule3 Figure1:Arrangementofthe9GPRradars.TheGPRsensorisatime-domain,transientsignalradarthatgivestargetsignalresponseinformationofadi erentnaturethanthatfrommoreconventionalcontinuous-waveradars.TheGPRhasapulsewidthof1. 258-nanosecondfullwidthathalfmaximum(FWHM).Itsoperatingfrequencyrangeisfrom320kHztoabout2GHz,anditssamplingrateis136. 6GHz.Theelectromagneticdesignoftheimpulsera-diatingantennasIRAsgivestheverybroadbandradiationpropertiesthatallowfortherequiredtransientresponse.Theimpulsegeneratoremployedinthetransmitterisdesignedtohaveaveryfastriseandaslowdecayinordertoenhancebothhigh-frequencyandlow-frequencycomponentsofthesignals.Thespectrumoftheradarsignalandfurtherde-tailsofthehardwareGPRsystemaredocumentedin[31 ]. Thereceiversamplingsystemtransformstheveryfastreal-timereturnsignalsfromburiedobjectsintomuchslowersampled-timedatasignalsthataredigitized,transmitted,andprocessed.Inparticular,ateachlocation,adatavectorof2048samplesisacquired,whichisthendown-sampledto512pointsforstorageandprocessing.TheGPRacquiresavectorsampleinevery7. 5cmspatialdistance.Eachvectorsampleisthenpassedontothesoftwarealgorithmsforthedetectionoflandmine. TheGPRsensorsystemhas3modules,andeachmod-ulecontainsthreetransmit-receiveradarpairs.Eachmod-ulecoversone-meterwideandthe3modulestogethercoverathree-meterswathseeFigure1).Eachtransmit-receiveradarpairconsistsofapulsegenerator,atransmitantenna,areceiveantenna,alow-noisepreamplier,andasamplingunit.Asignaltriggergeneratorandthedelayblockpro-videsforthetriggersforthecompletesensorsuiteofallnineradars.Theantennadesignisbasedonthatoftheimpulsera-diatingantennaasdevelopedbytheAirForceResearchLab-oratory,Albuquerque,NewMexico[32 33 34 ].Itconsistsofaparabolicconductingdishthatisilluminatedbytwopairsoftransmission-linefedarmsfromadrivepointatthefocalpointoftheparaboloid.Thetransmitandreceiveantennashaveadiameterof0. 3m.Figure1showsthearrangementofthe9transmit-receiveradarpairs.Inordertoincreasethespatialcoverageincaseaminetargetislocatedbetweentwoadjacentradarpairs,eachreceiverreceivesnotonlythesignalfromitscorrespondingtransmitterbutalsothesignalfromtheleftadjacenttrans-mitter.Thisisaccomplishedbyallowingeachreceiveran-tennatooperatewithtwosamplersineachreceiveroperatingsimultaneouslywithitsdirectandleftadjacentpulsers.Wereferthereaderto[31 ]forthedetailsofthisarrangement. Landminesignal1002003004005006007008009001000500 400 300 200 100 Depthindex (a) 1002003004005006007008009001000Landminesignal60 50 40 30 20 10 Depthindex (b) Figure2:GPRdatainasinglechannel:(a)databeforedownsam-plingindepth;(b)dataafterdownsamplingindepthbyafactorof8.Inreal-timeoperationalmode,thevehiclethatcarriestheGPRsystemadvancesataspeedof9km/h,andtheradarpro-videsathree-meterdetectionswath.Forinstance,toscanandprocess3 500squaremeters,ittakesabout0. 5km/ (9km/h)or3. 33minutes.3.2.DatarepresentationTheGPRdataisarrangedina3Darray,withthecross-track,down-track,anddepthcorrespondingtothethreedimen-sionsinthearray.Thetotalnumberofcross-trackchannelsis17andeachchannelcoversapproximately17centimeters.Thedown-tracksamplingrateis7. 5centimeters/sample.TheGPRprovides512depthdatapointsineachsamplelocation.Hence,fora3-meter-times-500-meterlane,theGRRdatahasasizeof17 6667 512.Inordertoreduceprocessingtime,eachdatasamplevectorisdownsampledfrom512to64bykeepingoneoutofeveryeightdatapoints.Figure2(a) givesasegmentoftheoriginalGPRdatainacertainchannelwith512pointsindepth,andFigure2(b)isthedownsam-pleddatabyafactorof8.Figure3showstypicalA-scanswithandwithoutdownsampling.Frequency-domainanalysisin-dicatesthatthedepthdatapointsareoversampled.More-over,extensivestudyhasshownthatdownsamplingindepthdimensionbyafactorof8doesnotintroducemuchdegra-dationintheperformanceofthedetector.Weshouldnoteherethatthey -axisinFigure2andthex -axisinFigure3arerelated,butnotequal,totherealdepth.Computingtheactualdepthvalueswouldrequiretheknowl-edgeofthefrequencybandwidthandthedielectricconstantofthesoil.Tofacilitatereal-timeoperationwithparallelprocessingcapability,theprocessingisperformedindependentlyfromchannel1tochannel17ateachdown-tracksamplelocation.Processingbeginswithpreprocessingofthedatatoremove

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1871 50100150200250300350400450500DepthindexAmplitude 5 0 5 (a) 50100150200250300350400450500DepthindexAmplitude 5 0 5 (b) 102030405060DepthindexAmplitude 5 0 5 (c) 102030405060DepthindexAmplitude 5 0 5 (d) Figure3:A-scansofGPRdatabeforeandafterdownsampling:a)A-scanofbackgroundsignalbeforedownsampling,b)A-scanoflandmineandbackgroundsignalbeforedownsampling,c)A-scanofbackgroundsignalafter8:1downsampling,and(d)A-scanoflandmineandbackgroundsignalafter8:1downsampling.systemresponse,groundbounce,andnoise.TheHMMal-gorithmisthenappliedtogenerateanalarmcondence.4.REAL-TIMELANDMINEDETECTIONUSINGHMM4.1.DatapreprocessingPreprocessingisanimportantsteptoenhancetheminesignaturesfordetection.Ingeneral,preprocessingincludesground-levelalignmentandsignalandnoisebackgroundremoval.Intheproposedsystem,weassumethatnoiseismuchsmallerthanthebackgroundsignal.Infact,theGPRhardwarecomponentperformswaveformaveragingtore-ducebackgroundnoisesothatitissmallenoughtobeig-nored.Theremainingbackgroundsignalsincludetheself-antennacouplingandgroundreection.Ourpreprocessingtechniqueisdesignedtosuppressthisbackgroundsignal.Ourpreprocessingfollowstheshift-and-scalemodelpro-posedbyBrunzell[9 ],wherethecurrentbackgroundvec-torsampleisassumedtobeashiftedandscaledversionofabackgroundreference.Backgroundremovalthenrequirestheestimationofbothshiftandscaleparameters,whicharechangingfromsampletosample.Theoriginalshift-and-scalemodelassumestheshiftisaninteger.Inpractice,thisassumptionmaynotbeaccurateastheshiftingcanbeintheorderofsubpixels,andinterpolationisneededtoperformsubpixelshifting.Unfortunately,interpolationincreasesthecomputationsignicantly,andprohibitsreal-timeprocess-ing.Inthispaper,weproposeane cientsubpixelshiftandscalepreprocessinginfrequencydomainsothatsubpixelshiftingcanberealizedinasimplemannertoreducecom-putation.Thesubpixelshiftandthescalefactorareobtainedusingthemaximum-likelihood(ML)approach.Experimen-tally,wehavefoundthatsubpixelshiftingreducesthenum-beroffalsealarmsbyatleastafactorof1. 5whencomparedtoBrunzellsintegershifting.Letx n denotetherawGPRdatameasuredatasamplelo-cation,wheren isthedown-tracklocationindex.Sincetheprocessingisperformedindependentlyineachcross-trackchannel,theindexforthechannelhasbeendroppedforno-tationsimplicity.Thevectorx n containsthedatapointsatdi erentdepthbins,thatis,x n = [ x n (1), x n (2), ... x n M )] T whereM = 64isthetotalnumberofdepthbinsinthedown-sampleddataasdescribedinSection3.2.Thevectorx n is modeledasx n = b n + s n + n ,(3where b n representsthebackgroundsignal,s n istheresponseproducedbyaminetargetoraclutterobject,and n isavec-torofbackgroundnoise.Notethatthesignals n willbezerointhesamplelocationthatdoesnothavemineorclutterob-ject.Thebackgroundreturnisrelativelystableinnormalen-vironmentandisconsideredtocomefromaglobalgenericbackgroundvectorb = [ b (1), b (2), ... b M )] T .Duetothesurfaceroughnessasthevehiclemoves, b n ismodeledasascaledandshiftedversionofb ,thatis, b n = a n b n ,(4wherea n isthescalingfactorclosetounity, n istheamountofshiftindepthwhichisnotnecessarilyaninteger,andb n = [ b (1+ n ), b (2+ n ), ... b M + n ] T .Theshiftbetweentwosuccessivesamplesistypicallyverysmall,thatis, | n n 1 n ,andlessthananintegerinmostcases.Thisshiftandscalebackgroundmodelhasbeenusedpre-viouslybyBrunzell[9 ]forbackgroundremoval,wheretheshiftisassumedtobeaninteger.Theproblemismorechal-lengingheresincetheshiftisnotnecessarilyaninteger.Thebackgroundreturnismuchstrongerthanthesignals n and dominatesthemeasurement.Theobjectivehereistoremovethebackgroundsignalcomponentsothattheminesignaturebecomesapparentfordetection.Thebackgroundremovalproblemcanbeconsideredasndingthepaira n n )givenx n and b ,sothatthebackgroundresponsecanbesubtractedout.Intheabsenceofthesignals n andassumingGaussian n ,themaximum-likelihoodsolutionisfoundbyminimiz-ing[9 ] J a n n = x n a n b n T W x n a n b n ,(5

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1872EURASIPJournalonAppliedSignalProcessing 51015202530IntensityRelativedown-trackscannumber60 50 40 30 20 10 (a) 51015202530IntensityRelativedown-trackscannumber60 50 40 30 20 10 (c) 51015202530IntensityRelativedown-trackscannumber60 50 40 30 20 10 (e) 51015202530IntensityRelativedown-trackscannumber60 50 40 30 20 10 (b) 51015202530IntensityRelativedown-trackscannumber60 50 40 30 20 10 (d) 51015202530IntensityRelativedown-trackscannumber60 50 40 30 20 10 (f) Figure4:Preprocessedsamples:a)datafromaplasticmineburiedat2 ,b)preprocessedresultofa),c)datafromaplasticmineburiedat3 ,d)preprocessedresultofd),e)datafromametalmineburiedat6 ,and(fpreprocessedresultofe).whereW istheweightingmatrixequaltoE [ n T n ] 1 .Opti-mizing5 )withrespectto a n yields a n = b n T Wx n b n T Wb n (6) Substituting6 into5 )givesJ n = x T n Wx n b n T Wx n 2 b n T Wb n (7) Because n isnotnecessarilyaninteger,theelementsofb n areformedbyinterpolation.Thatis,b i + n = M m = 1 b m )sinc i + n m i = 1,2,... M (8) wheresinc = sin( / ).Asaresult,7 isanonlinearfunctionwithrespectto n andnumericalsearchisneces-sarytothesolution n thatminimizes7 ).Equation8 requiresM 2 multiplicationstogenerateb n )foragiven n Assumingthesearchspaceof n has L values,thenatasinglesamplelocationndingtheoptimumsolutionof n requiresanorderofM 2 L operations,whichiscomputationallyveryintensive,andprohibitsreal-timeprocessing.Asanalterna-tive,weproposetouseafrequency-domain-basedapproachtoreducethecomputation.Thefrequency-domainrepresentationof8 )isB n = diag e 1 n e 2 n ... e M n B ,(9whereB n )andB arecolumnvectorscorrespondingtothediscreteFouriertransformsofb n )andb ,and m = 2 m 1) /M m = 1,2,... M .Furthermore,W infrequency

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1873 domainbecomestheinverseofadiagonalmatrixwhosem th diagonalelementisP m ),thepowerspectraldensityof n atfrequency m .Hence,byrepresenting7 inthefrequencydomainandapplyingtheParsevaltheorem[18 ],theobjec-tivefunctiontobemaximizedtoobtain n becomesJ n = M m = 1 1 P m X n m B n m 2 ,10)wheretheconstantsthatareindependentof n in7 )havebeenignored,andthesuperscript representscomplexconjugate.Notethat| B n m | 2 =| B m | 2 hasbeenusedsothatthedenominatorin7 isindependentof n ,andisthereforeignored.In10 ), X n m )andB n m )representthe m thelementofX n and B n ).Substituting9 into10 reducestoJ n = M m = 1 1 P m X n m B m e m n 2 (11) Notethatthevalueinsidethebracketisindependentof n andneedstobecomputedonce.Foratrialvalue n ,( 11 requiresonlyM +1complexmultiplications.Thecomputationcanfurtherbereducedbyusingthefactthat | n n 1 n .Atthepreviousspatialinstantn 1, weobtained n 1 .Atthecurrentinstantn ,wedeterminetherelativetranslation n = n n 1 bymaximizing J n = M m = 1 1 P m X n m X n 1 m e m n (12) Thesolutionof n isthenequalto n 1 + n .ThesearchspacenowreducesfromL of n to L of n ,whereL
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1874EURASIPJournalonAppliedSignalProcessing Figure5displaysahyperboliccurvesuperimposedonapre-processedmetalminesignaturetoillustratethefeaturesofatypicalminesignature.LetS x y z denotethepreprocessedthree-dimensionalGPRdataasillustratedinFigure6.Thedown-tracksecondderivativeisrstestimatedontherawdatausing D y x y z = S x y +2,z )+2 S x y +1,z 2 S x y 1, z S x y 2, z 3 D yy x y z = D y x y +2,z )+2 D y x y +1,z 2 D y x y 1, z D y x y 2, z 3 (15) Thederivativevaluesarethennormalizedalongthey direc-tionusingN x y z = D yy x y z x z x z ,16)where x z )and x z aretherunningmeanandstandarddeviationupdatedusingabu erofscansavailableduringsystemoperation.Thedown-trackdimensionistakenasthetimevariableintheHMMmodel.Thegoalistoproduceacondencethatamineispresentatvariouspositions,x y ),onthesurfacebeingtraversed.TointotheHMMcontext,asequenceofobservationvectorsmustbeproducedforeachpoint.Theseobservationvectorsencodethedegreetowhichedgesoccurinthediagonalandantidiagonaldirections.Theobservationvectoratapointx s y s consistsofasetof15featuresthatarecomputedonanormalizedarrayofGPRdataofsize32 8.Letx s and y s begivenandletA denotethearrayA = A y z = N x y z ),(17)wherex = x s y ={ y s 3, ... y s +4 } ,andz ={ 1,2,... ,32} ThearrayA isthenbrokenintopositiveandnegativepartsaccordingtotheformulasA + y z = A y z )ifA y z > 1, 0otherwise,A y z = A y z )ifA y z < 1, 0otherwise. (18) Next,foreachpointinthepositiveandnegativepartsofA thestrengthsofthediagonalandantidiagonaledgesareesti-matedandareusedtodenethe15-dimensionalobservationvectorassociatedwiththepointx s y s .Wereferthereaderto[12 ]foramoredetaileddescriptionoftheobservationvector.4.3.ImprovedcontinuousHMM-basedclassierforlandminedetectionTheproposedHMMclassierconsistsoftwoHMMmod-els,oneformineandoneforbackground.Theminemodel, z (depth) x (cross-track)o y (down-track) Figure6:AcollectionoffewGPRscans. m ,isdesignedtocapturethehyperbolicspatialdistributionofthefeatures. m has3stateswhichcorrespondtotheris-ingedge,at,anddecreasingedge.Eachstateisrepresentedby3Gaussiancomponents.Theminemodelisillustratedin Figure7.Thebackgroundmodelisneededtocapturethebackgroundcharacteristicsandtorejectfalsealarms.Eachofthe17channelsistreatedindependentlyfromtheoth-ers,andhasitsownbackgroundmodel, b c .Inadditiontoallowingeachchanneltohaveamodelthatreectsitsowndata,thisdecouplingallowsthechannelstobeprocessedinparallel,andthusfacilitatingreal-timeoperation.All b c (for c = 1, ... ,17)have3statesand3Gaussiancomponentsperstate.ThemodelarchitectureisillustratedinFigure8. EachHMMproducesaprobabilitybybacktrackingthroughmodelstatesusingtheViterbialgorithm[22 ].Theprobabilityvalueproducedby m b c canbethoughtofasanestimateoftheprobabilityoftheobservationsequencegiventhatthereisamine(background)present.TheproposedHMMclassierisbasedonapreviousworkbyGaderetal.[12 ].Inthefollowing,weonlyoutlinethemodicationswemadetothebaselinesystemtoimproveitsperformanceande ciency.

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1875 Minestate1Minestate3Minestate2StatesMinestate1Minestate2Minestate3x 1 x 2 x 3 x 14 x 15 Figure7:IllustrationoftheHMMminemodel.4.3.1.ObservationsequencepreprocessingMostmineshavesignaturesofdi erentsizes,andtheirdis-tributioncannotbecapturede cientlybxednumberofobservations.Toaddressthisproblem,thebaselinesys-temusesaminemodelwith5states.Therstandlaststatesarebackgroundstates.Duringtesting,eachsequenceisal-lowedtostartineitherthebackgroundstateortherstminestate.Moreover,twooptimalstatesequencesarecom-puted:oneassumingthemodelassignsthelastobservationtothethirdminestate,andtheotherassumingthelastob-servationisassignedtothebackgroundstate.Thestatese-quencewiththehighestprobabilityistakenasthemodelout-put. Theproposedsoftwaresystemusesobservationse-quencesofvariablelength.Thisapproachismoree cientasonly3statesareneededfortheminemodel,andonlyoneop-timalstatesequenceisneeded.Initially,eachsequencecan-didatehasaednumberofobservations,T max .Beforefeed-ingthesequencetotheHMMclassier,weignorealllead-ingandtrailingobservationswithweakfeaturevectors.Inotherwords,weexcludeobservationO t fromthesequenceif O t min .ThisprocessresultsinasequenceoflengthT whereT
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1876EURASIPJournalonAppliedSignalProcessing GradientfeatureextractionHMM mine model HMM backgroundmodel+ Figure8:IllustrationoftheHMM-basedmodelarchitecture. ReadmineandbackgroundsignaturelibrariesEstimateinitialminemodelparametersusingBWprocedureEstimateinitialbackgroundmodelparametersusingBWprocedureRepeatForeachsignatureobservationsequenceO Letc denotethechannelfromwhichsignatureisextractedUseViterbiproceduretocomputeP O | m )& P O | b c IfP O | m > = P O | b c classifyO asmineElseClassifyO asbackgroundIf signatureismisclassiedLetr denotethecorrectmodelLetw denotetheincorrectmodelForeachobservationO t ofthesequenceO i = stateassignedtoO t bymodelr k = mostprobablecomponentofstatei ofmodelr k = argmaxm = 1, ... M i b r m O t r ki (new) = r ki (old+ x t r ki (old) j = stateassignedtoO t bymodelw l = mostprobablecomponentofstatej ofmodelw l = argmaxm = 1, ... M j b w m O t w lj (new) = w lj (old) x t w lj (old) (20) Endforloop Endifloop Endforloop ReestimateminemodelparametersusingBWprocedureReestimatebackgroundmodelsparametersusingBWprocedureUntil(convergenceormaximumno.ofpassesreached) Algorithm1:Correctivetrainingformine/backgroundHMMmodels.observed,theparametersof m and b c areadjustedtoreducethelikelihoodofrepeatingthiserror.Inparticular,theGaus-sianmeansofthemostprobablecomponentofthestatesintheViterbipathsareadjustedusinganLVQ-type[35 ]learn-ingrule.Theabovestepsarerepeateduntilallthetrain-ingdataisclassiedcorrectly,orthemaximumnumberofpassesisreached.TheproposedcorrectivetrainingalgorithmisoutlinedinAlgorithm1. Inthistrainingalgorithm,20 )isanLVQ-type[35 ] learningrule.ThemeanvectorsoftheGaussiancomponentsaremovedclosertotheobservationsofthecorrectlyclassi-sequences,andfurtherfromtheobservationsofthemis-classiedsequences.In(20 ),theconstant isthelearningrate,andhassimilarbehaviorasinstandardLVQalgorithms.If istoosmall,thenseveralpasseswouldbeneededforthealgorithmtoconverge.Ontheotherhand,if istoolarge,thetrainingalgorithmmaynotconvergeaslargecorrectionsmadebysomesequencesmaybereversedbyothersequences.Inthispaper,wereporttheresultsusing = 1 0e-3fortheminemodel,and = 1 0e-4forthebackgroundmodel.Thereasonforusingasmallerrateforthebackgroundisthatthismodelis,ingeneral,lessconsistentthantheminemodel,andthemagnitudeoftheerrorsecondpartof20 isusuallylargerthanthatcausedbytheminemodel.

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1877 Let b c bethebackgroundmodelofchannelc estimatedusingtrainingdata, c ij = meanofcomponenti ofstatej of b c C c ij = covariancematrixofcomponenti ofstatej of b c n ij = numberoftrainingobservationsthatcontributedtotheestimationof c ij and C c ij LetN ij = K n ij ; S ij = N ij c ij ; SSqij = N ij [ C c ij + c ij c ij T ]denotethesu cientstatisticsofGaussiancomponenti ofstatej ForeachtestedobservationsequenceO withConfO < Min ConfForeachobservationO t of O j = stateassignedtoO t i = mostprobablecomponentofstatej : i = argmaxm = 1, ... M j b mi O t S ij = S ij + x t SSqij = SSqij + x t x T t N ij = N ij +1 EndEnd c ij = Sumij /N ij ; C c ij = SumSqij /N ij c ij c ij T ;fori = 1, ... N and j = 1, ... M i Algorithm2:Incrementalupdateofthebackgroundmodels.Asinmostlearningalgorithms,thenumberoftrain-ingiterationsfortheproposedcorrectivetrainingalgorithmisimportant.Generally,thisnumberwoulddependonthelearningrate, ,thedielectricconstantofthesoilfromwhichthetrainingsignatureswereextracted,theconsistencyofthetrainingsignatures,andthelevelofvariationsbetweenthesignaturesusedfortheinitialtrainingandthesignaturesusedforthesubsequentcorrectivetraining.Ifthenumberofcorrectivetrainingiterationsisnotsu cient,theparame-tersofthemodelswouldnotadaptsu cientlytothegivensite.Ontheotherhand,iftoomanycorrectiveiterationsareapplied,themodelsmaygetovered.Thestandardap-proachestoaddressthisissueistoeitherstopthetrainingwhentheperformancedoesnotimprovesignicantly,oruseacrossvalidationdatasetandstopthetrainingwhentheper-formanceonthevalidationsetnotusedfortraining)startstodecrease.Currently,oursystemusestheformerapproachasourlabeledtrainingdataisnotlargeenoughtobesplitintotrainingandcrossvalidationsets.Experimentally,wehavefoundthatonly5to10iterationsareneededwhenthecorrectivetrainingalgorithmisappliedo inetothetrainingsignatures.Applyingthealgorithmformoreiterationsdoesnotimprovetheperformanceofthedetectoranyfurther.Thecorrectivetrainingproceduredescribedaboveop-eratesonasignaturelibrary,andisfortheo inemode.Itcanbeeasilymodiedtooperateinareal-timemodeandadapttheHMMstodi erentsitesandenvironmentsusingfeedbackonwhichmeasurementsareminesandfalsealarmsoncetheyaredug.Inthiscase,insteadofreadingthesigna-tures,thealgorithmstartsbyreadingthelanegroundtruth.Then,thelanedataisprogressivelyreadandprocessedastheGPRmountedvehiclemoveroverthelane.Asintheo ine mode,theparametersareadjustedwheneveramisclassica-tionoccurs.Toperformmorethanoneiterationofcorrectivetraining,onecouldeitherdriveoverthelanemultipletimes,orsimplystorethedataandreprocessitfewmoretimeswhentheendofthelaneisreached.Inthisreal-timemode,themodelparametersareadoptedtonewdatathatwasnotincludedintheinitialtrain-ingphase.Thus,itisexpectedthatmoreiterationswouldbeneeded.Experimentally,wehavefoundthat,forallthecali-brationlanes,10to20correctivetrainingiterationsaresuf-cient.Applyingthealgorithmformoreiterationsdoesnotimprovetheperformanceanyfurther.4.5.AdaptivebackgroundmodelTheminemodeliswelldenedandneedstobedesignedtocapturethehyperbolicminesignatures.Thebackgroundmodel,ontheotherhand,isnotwelldened.Itisneededtomodelthebackgroundcharacteristicssoastoreducethenumberoffalsealarms,however,itisalmostimpossibletospecifythecharacteristicsofthismodel.Thisisbecausethebackgroundmodelisa ectedbyseveralfactorssuchasdif-feringsoilconditions,temperatureandweatherconditions,andvaryingterrain.Infact,thebackgroundcanchangebe-tweenthestartandtheendofthesametestlaneasthehard-waresettingsandweatherconditionscanchange.Sinceitisnotpossibletocollecttrainingdatathatcoversalldi erentsettings,oursystemsusesanadaptivebackgroundmodel.Ouradaptiveapproachinvolvestwomainsteps.4.5.1.AdaptivedatanormalizationTomaintainthesamedynamicrange,anduseconstantthresholds,weadaptivelynormalizethepreprocesseddatasothatitsvaluesarenormallydistributedwithzeromeanandunitvariance.Thedatastatisticsaredynamicallyupdatedus-ingabu erofthemostrecentobservations.Observationse-quencesareaddedtothebu eronlyiftheirlikelihoodofbe-longingtothebackgroundmodelishigh.Wethebu er sizeto50observations,andasthebu ergetsfull,newobser-vationswouldreplacetheoldones.4.5.2.IncrementalupdateofthebackgroundmodelsAninitialbackgroundmodel, b c ,isestimatedforeachchan-nel, c ,byapplyingthecorrectivetrainingprocedureonthetrainingsignatures.Whiletesting,observationsequenceswithhighP O | b c andlowP O | m areusedtoadjusttheparametersofthebackgroundmodelofchannelc .Inpartic-ular,weuseAlgorithm2.

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1878EURASIPJournalonAppliedSignalProcessing Table1:Summaryofthethreedatacollectionsusedintheexperiments. CollectionLocationContent (1)SignaturesSite12945mineobservationsequences.5737falsealarm/backgroundobservationsequences. (2)LanedataSite2Lane4100m 3m14mines21passesLane6100m 3m10mines24passesLane8100m 3m19mines20passesLane9100m 3m18mines18passes (3)LanedataSite3Lane51200m 3m21mines6passesLane52200m 3m16mines6passesLane56200m 3m21mines6passes 5.EXPERIMENTS5.1.ExperimentaldataGPRdatacollectedfromthreedi erentsitesintheUnitedStateswasusedinourexperiments.Wewillrefertotheseascollection1,collection2,andcollection3,respectively.Col-lection1containsminesandfalsealarms/backgroundsigna-turesextractedfromdatacollectedatsite1.Thesesignatureswereselectedusingacombinationofgroundtruthandvi-sualexamination,andconsistof2945minesand5737falsealarms/backgroundobservationsequences.Amoredetaileddescriptionofthissignaturelibraryandtheextractionpro-cesscanbefoundin[12 ].ThiscollectionisusedtolearntheinitialmineandbackgroundHMMmodelparametersusingthebasicBaum-Welchalgorithm.Collections2and3containGPRlanedatacollectedfromsites2and3,respectively.Someoftheselaneswereusedforcorrectivetraining,andtheremainingfortesting.Test-ingandadaptingthemodelparametersonlanesisthemostrepresentativeofreal-worldoperationalmode.Site2has4laneslabeledlane4,6,8,and9.Site3has3laneslabeledlane51,52,and56.Eachlaneis3mwide,anditslengthvariesfrom50to200m.Thegroundtruth,thatis,loca-tionofthemines,ofthesecalibrationlanesisavailable,andweuseitonlyduringthecorrectivetrainingorintheeval-uationofthealgorithm,andnotintheHMMtestingal-gorithmitself.Multipledataleswerecollectedfromeachlane.Eachle,referredtoasonepass,correspondstorun-ningavehicle-mountedGPRsystemoverthelane.Ato-talof83passeswerecollectedfromsite2,andonlyoneofthesepasses(fromlane4)wasusedforcorrectivetrainingtoadapttheHMMstothissite.Collection3includes18passes,andoneofthepasses(fromlane51)wasusedfortraining.Table1summarizesthedatacollectionsusedinourexperi-ments. Weshouldnoteherethatalthoughthelanesusedinourexperimentsdonothaveexplicitlyemplacedclutter,theyweresetuptorepresentrealon-roadconditionsthatavehicle-mountedminedetectionsystemwillencounter.Thus,theydoincludeclutterobjectssuchasvoid,rocks,andprobablysomemetalpieces.5.2.BasicHMMtrainingThesignaturelibraryi.e.,collection1wasusedtotrainthebasicHMMmodels.Usingthiscollection,BWalgorithmwasusedtoestimatetheHMMparameters = m b ),where m isestimatedfromtheminesignaturesand b isestimatedfromthefalsealarms/backgroundsignatures.Wewillrefertotheseasthebaselinemodels,orsimply base 5.3.CorrectiveHMMtrainingusingthesignaturelibraryUsing base asinitialmodelparameters,weappliedthecor-rectivetrainingproceduretothesignaturelibraryandad-justedtheparameterstoreducethenumberofmisclassiedsignatures.Atotalof10iterationswereneededforthepa-rameterstostabilize.Wewillrefertothesemodelsas Sig. 5.4.CorrectiveHMMtrainingusinglanedataTherationaloftheproposedtrainingapproachistoadaptthemodelparameterstodi erentgeographicalsitesthathavedi erentcharacteristicsduetovariationsinsoiltypeandotherconditions.Thus,wehaveselectedonepassfromcol-lection2anduseditalongwithitsgroundtruth)toadaptthebaselineHMMstothissite.Thetrainingpasswasselectedfromlane8asthislanecontainsmoremineswithmoreva-riety.Inallexperimentsreportedinthispaper,atotalof20correctivetrainingiterationswereperformed,andinterme-diatemodelparametersweresavedaftereachiteration.Wewillrefertothesemodelsas S2-L8 k i.e.,modelsadaptedtosite2usinglane8afterk iterations).Similarly,wehaveadaptedthebaselineHMMstosite3byapplyingthecorrectivetrainingusingonepassfromthiscollection(fromlane51).Forthissite,weobtainedtheinter-mediatemodels S3-L51 k ). 5.5.ExperimentalresultsInthissection,wepresent,analyze,andcomparetheresultsobtainedusingthecorrectivetrainingprocedurewiththoseobtainedusingthebaselinemodel.Ourresultscouldnotbecomparedwiththebasicsystemintroducedin[12 ],asthesesystemsusedi erentGPRprototypes,andthus,havepre-processedthedatadi erently.However,weshouldpointout

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1879 thatthetwosystemsareverysimilar.Themajordi erencesaretheadditionalpre-andpostprocessingstepsoutlinedinSection4.3.Thesestepsdonota ectthedetectionresultssignicantly.Theyareaddedmainlytoreducetheexecutiontime,andthus,enablereal-timeimplementationandtesting.Thisisbecause1)thesequencesarenolongerrequiredtohaveaconstantlengthof15(maximumlength);2)only3not5statesareneededfortheminemodel;and3)severalsequencesarerejectedwithouttestingthemwiththeback-groundmodelsusingtheViterbialgorithm.Theperformanceofthedi erentmodelparameterswasscoredintermsofprobabilityofdetectionPD)versusfalsealarmrateFAR).Condencevalueswerethresholdedatdi erentlevelstoproducereceiveroperatingcharacteristics(ROCcurves.Foragiventhreshold,amineisdetectedifthereisanalarmwithin0. 25metersfromtheedgeoftheminewithcondencevalueabovethethreshold.Givenathreshold,thePDforalaneorasetoflanesisdenedtobethenumberofminesdetecteddividedbythetotalnumberofmines.TheFARisdenedasthenumberoffalsealarmspersquaremeter.Figure9ashowstheoverallROCsforallofthe83passesofcollection2.TheROCsaredisplayedforthecondencevaluesgeneratedusingthebaselinemodel, base (nocorrec-tivetraining),the Sigmodelcorrectivetrainingusingsig-naturelibrary),andthe S2-L8 k )models(k iterationsofcor-rectivetrainingusingonepassfromcollection2).Ascanbeseen,whencomparedtothe base ROC,the Sigand S2-L8 k ROCsareshiftedleft(i.e.,lowerFARforthesamePD)andshiftedup(higherPDforthesameFAR).Thus,onecanconcludethatcorrectivetrainingimprovestheoverallde-tectionrate.Toquantifytheimprovementinthedetectionrate,wecomputetheareaundertheROCinthe[0,0. 02]FARrange.1 Fortherestofthispaper,wewillusethetermperformancetorefertothisarea.Aperfectdetector(detectsallthemineswithnofalsealarms)wouldhaveanareaof0. 02. Figure9b displaysthevaluesoftheseareasfortheROCsofthedi er-entmodels.Ascanbeseen,theareajumpsfrom0. 013(forthebaselineparameters)to0. 0134forthe Sigparameters,andto0. 014 S2-L8 (20),achievinganoverallperformancegainofabout10%.Ascanbeseen,theperformancecurvestartstoattenafter15iterations.Performingthecorrectivetrainingformorethan20iterationsdoesnotimprovetheperformanceanyfurther.Figure9displaystheresultsaveragedover83passes.Theperformance(measuredbytheareaundertheROC)fortheindividualpassesvariessignicantly.Forinstance,forsomepasses,theperformanceremainsconstant.Thesepassesareusuallyeitherclean,withallmineseasilyde-tectable,orverynoisywithseveralweakminesignatures.Thus,theperformanceiseitherclosetooptimal,andcan-notbeimprovedanyfurther,orpoorandcannotbeim-proved,asmanyoftheminescouldnotbedetectedusing 1 Theperformancecriterionforthevehicle-mountedminedetectionsys-temtechnologywassetto0. 02/m 2 FARat90%PD,andisdescribedin[36 ]. 00 0050. 010. 0150. 020. 0250. 03 FAR/ m 2 0 5 0 55 0 6 0 65 0 7 0 75 0 8 0 85 0 9 0 95 1 PD base sig S2 L8 (1iter.) S2 L8 (3iter.) S2 L8 (5iter.) S2 L8 (10iter. (a) BaseSig135101520No.ofcorrectivetrainingiterations0 0125 0 013 0 0135 0 014 0 0145 AreaunderROC (b) Figure9:AverageperformanceoftheHMMdetectorwithdi er-entmodelparametersonthe83passesofcollection2.a)ROCswithandwithoutcorrectivetraining.b)Improvementintheper-formance(areaunderROCinthe[0,0.02]FARrange)versusnum-berofcorrectivetrainingiterations.thecurrentpreprocessingandfeaturerepresentationtech-niques. Formostpasses,theperformanceimproves.Figures10 and 11 displaytheresultsfortwodi erentpassesoverlanes4and6,respectively,wheretheperformanceimprovesbyabout50%.ForFigure10,theimprovementoccursaftertheinitialcorrectivetrainingwiththesignaturelibrary,andmoretrainingwiththelanedatadoesnota ecttheresults.Ontheotherhand,forFigure11,nosignicantimprove-mentwasobtainedafterthecorrectivetrainingwiththesig-naturelibrary.Thelargestperformancegainwasobtainedusing S2-L8 (10).

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1880EURASIPJournalonAppliedSignalProcessing 00 0050. 010. 0150. 020. 0250. 03 FAR/ m 2 0 5 0 55 0 6 0 65 0 7 0 75 0 8 0 85 0 9 0 95 1 PD base sig S2 L8 (1iter.) S2 L8 (3iter.) S2 L8 (5iter.) S2 L8 (10iter. (a) BaseSig135101520No.ofcorrectivetrainingiterations0 01 0 011 0 012 0 013 0 014 0 015 0 016 0 017 0 018 0 019 0 02 AreaunderROC (b) Figure10:PerformanceoftheHMMdetectorononepassfromlane4.(a)ROCswithandwithoutcorrectivetraining.b)Improve-mentintheperformance(areaunderROCinthe[0,0. 02]FARrange)versusnumberofcorrectivetrainingiterations.Wehavealsogroupedthepassesbylanes,andgener-atedoneROCforeachlane.Theperformanceofthedi er-entlanesisshowninFigure12(a).Ascanbeseen,theper-formancevariessignicantly.Lane4hasanalmostperfectperformance,whilelane9hastheworstperformance.Thistypeofperformanceisexpectedsincelane4containsmainlymetalmines,whilelane9containsmainlysmallplastic-casedmines.Lanes6and8containamixtureofbothtypesofmines.Forallthelanes,theimprovementduetothecor-rectivetrainingisnotobviousinFigure12(a).Thisisduetotherelativelylargevariationintheverticalaxis.Toout-linethee ectofthecorrectivetraining,inFigure12(b),wedisplaytheareasobtainedwiththecorrectivetrainingmod00 0050. 010. 0150. 020. 0250. 03 FAR/ m 2 0 5 0 55 0 6 0 65 0 7 0 75 0 8 0 85 0 9 0 95 1 PD base sig S2 L8 (1iter.) S2 L8 (3iter.) S2 L8 (5iter.) S2 L8 (10iter. (a) BaseSig135101520No.ofcorrectivetrainingiterations0 0125 0 013 0 0135 0 014 0 0145 0 015 0 0155 0 016 0 0165 0 017 AreaunderROC (b) Figure11:PerformanceoftheHMMdetectorononepassfromlane6.(a)ROCswithandwithoutcorrectivetraining.b)Improve-mentintheperformance(areaunderROCinthe[0,0. 02]FARrange)versusnumberofcorrectivetrainingiterations.elsnormalizedwithrespecttotheareaofthecorrespond-ingbaselinesystem.Ascanbeseen,theimprovementvariesfrom4%to27%.Thebestimprovementisobtainedforlane9,whichwasthemostdi cultlane.Thisillustratestheabilityoftheproposedcorrectivetrainingtoadaptthemodelsparametersandimprovethedetectionofdi cult mines. Datacollection2hasatotalof83passesthatwerecol-lectedoverthreedi erentdates.Therst20passeswerecol-lectedonApril8and9,thenext27passeswerecollectedonJune11and12,andthelast36passeswerecollectedonJune27and28.Oneachdate,datawascollectedfromall4lanes.WehavegeneratedoneROCforeachdateusingthedi erent

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1881 BaseSig135101520No.ofcorrectivetrainingiterations0 004 0 006 0 008 0 01 0 012 0 014 0 016 0 018 0 02 AreaunderROCLane4Lane6Lane8Lane9 (a) BaseSig135101520No.ofcorrectivetrainingiterations1 1 05 1 1 1 15 1 2 1 25 1 3 1 35 NormalizedareaunderROCLane4Lane6Lane8Lane9 (b) Figure12:AverageperformanceoftheHMMdetectoroncollec-tion2groupedbylanes.(a)AreaunderROCsinthe[0,0. 02]FARrangeversusnumberofcorrectivetrainingiterations.b)Normal-izedareasunderROCinthe[0,0. 02]FARrangewithrespecttotheareaofthebaselinesystem.HMMs. Figure13(a)displaystheperformanceoneachdate.Ascanbeseen,eventhoughthesamelaneswereused,theperformanceonthedi erentdatesvaries.Thisisduemainlytothedi erentweatherandsoilconditions,andpossiblydif-ferentradarsettings,onthedi erentdates.Figure13(b)dis-playsthenormalizedareastoemphasizetheimprovementsduetothecorrectivetraining.Theimprovementvariesfrom4%to12. 5%.Itisinterestingtonoticethat,inthiscase,thebestimprovementAprildata)doesnotcorrespondtothedatethathadtheworstperformanceJune27and28data).ThiscanbeexplainedbythefactthatthepassusedforthecorrectivetrainingwascollectedinAprilalso.Thus,thesereBaseSig135101520No.ofcorrectivetrainingiterations0 012 0 0125 0 013 0 0135 0 014 0 0145 0 015 AreaunderROCJune11&12April8&9June27&28 (a) BaseSig135101520No.ofcorrectivetrainingiterations1 1 05 1 1 1 15 NormalizedareaunderROCApril8&9June27&28June11&12 (b) Figure13:AverageperformanceoftheHMMdetectoroncollec-tion2groupedbydates.(a)AreaunderROCsinthe[0,0. 02]FARrangeversusnumberofcorrectivetrainingiterations.b)Normal-izedareasunderROCinthe[0,0. 02]FARrangewithrespecttotheareaofthebaselinesystem.sultsshowthatthecorrectivetrainingcouldbeusedtoadaptthemodelparameterstothedi erentsoilandenvironmentconditions.Theaboveexperimentswererepeatedusingcollection3andtheHMMsobtainedbyperformingcorrectivetrainingusingonepassfromlane51ofthiscollection( S3-L51 k ), k = 1, ... ,20).Theresultsandconclusionswerecompa-rabletothoseobtainedforcollection2.Figure14(a)showstheoverallROCsforallofthe18passesofcollection2.TheROCsaredisplayedforthecondencevaluesgeneratedusingthebaselinemodel, base ,and S3-L51 (10)models.Nosigni-cantimprovementcanbenoticedusingmodelslearnedwith

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1882EURASIPJournalonAppliedSignalProcessing 0246810121416182010 2 FAR/ m 2 0 5 0 55 0 6 0 65 0 7 0 75 0 8 0 85 0 9 0 95 0 1 PD base S3L51(10iter. (a) BaseSig13510No.ofcorrectivetrainingiterations0 015 0 0155 0 016 0 0165 0 017 0 0175 AreaunderROC (b) Figure14:AverageperformanceoftheHMMdetectorwithdi er-entmodelparametersonthe18passesofcollection3.(aROCswithandwithoutcorrectivetraining.b)Improvementintheper-formance(areaunderROCinthe[0,0. 02]FARrange)versusnum-berofcorrectivetrainingiterations.morethan10iterationsofcorrectivetraining.Figure14(b) showstheareaundertheROCinthe[0,0. 02]FARrange.Ascanbeseen,after5iterations,theoverallperformanceim-provesbyabout8%.Figure15displaystheperformancegroupedbylanes.Asincollection2,sincethelaneshavedi erentmixturesofminetypes,theirperformancevaries.Lane51benetedmostfromthecorrectivetraining.Thisisduetothefactthatthislanehadtheworstinitialperformance,sothereismoreroomforimprovement.Also,thepassthatwasusedforcorrectivetrainingwasextractedfromthislane.Thus,thetrainedmod-elswereadaptedtothislane.Itisinterestingtonoticethattheperformanceonlane51using Sigisslightlyworsethantheperformanceusing base .Thismaybeduetothefactthatthedatafromthislanehasdi erentcharacteristicsthanthe BaseSig13510No.ofcorrectivetrainingiterations0 014 0 0155 0 015 0 0155 0 016 0 0165 0 017 0 0175 0 018 0 0185 AreaunderROCLane51Lane52Lane56 (a) BaseSig13510No.ofcorrectivetrainingiterations0 98 1 1 02 1 04 1 06 1 08 1 1 1 12 1 14 NormalizedareaunderROCLane51Lane52Lane56 (b) Figure15:AverageperformanceoftheHMMdetectoroncollec-tion3groupedbylanes.(a)AreaunderROCsinthe[0,0. 02]FARrangeversusnumberofcorrectivetrainingiterations.b)Normal-izedareasunderROCinthe[0,0. 02]FARrangewithrespecttotheareaofthebaselinesystem.signaturelibrary.Thus,amodelthatminimizesthemisclas-sicationofthesignaturesmaynotbesuitedforasitewithdi erentcharacteristics.6.CONCLUSIONSAreal-timesoftwaresystemforlandminedetectionus-ingground-penetratingradarisproposedandevaluated.

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1883 Thesystemincludesthreemaincomponents:preprocessing;HMM-baseddetector;andcorrectivetraining.Theprepro-cessingcomponent,whichisneededtoenhancetheminesignatures,requirestheestimationofsubpixelshiftandscalefromonevectorsampletothenext.Toreducethecompu-tationalrequirementsandfacilitatereal-timeimplementa-tion,weproposedane cientfrequency-domain-basedpro-cessing.TheHMMdetectorisanimprovementofaprevi-ouslyproposedsystembaseline).Itincludesadditionalpre-andpostprocessingstepsoftheobservationsequencestoim-provethetimee ciencyandenablereal-timeapplication.Italsotreatsthesensorschannelsindependently,andusesonebackgroundmodelperchannel.Thisallowsparallelprocess-ingofthedi erentchannelsandbetteradaptation.Thecor-rectivetrainingcomponentisusedtoadjusttheinitialmodelparameterstominimizethenumberofmisclassicationse-quences.Twocorrectivetrainingscenarioswereused.Therstoneiso ine,andisappliedtoasignaturelibrarytoad-justtheparametersofagenericmodel.Thesecondscenariomimicsareal-worldoperationalmodewhere,feedbackonwhichmeasurementsareminesandfalsealarmsoncetheyaredug,wouldbeusedtoadapttheinitialmodelstospecicsitesandenvironments.Theproposedsystemwastestedinreal-timesettings.Ex-tensiveexperimentsindicatethatthecorrectivetrainingcanimprovetheoverallperformancebyabout10%,andthatforsomeindividuallanes,theperformancegaincanreachupto50%.Moreover,thebestgaininperformanceisusuallyob-tainedforthedi cultlanesthathadlowminedetectionandhighfalse-alarmratesusingthebaselineparameters.Inthecurrentsystem,onepass(fromonelane)wasusedtoadaptthemodelparameterstoallthedatacollectedfromonesite.Inthefuturework,wewillexperimentwithadapt-ingtheparameterstoindividuallanesusingasmallcalibra-tionsegmentfromeachlane.Anotherdirectionforfutureresearchinvolvesbuildingandlearningdi erentmodelsforthedi erentminetypese.g.,plasticversusmetal).Thismayrequireextractingmultiplefeaturesets,andusingdi erentsubsetstocharacterizethedi erentmodels.Finally,weshouldnotethatouradaptivesystemcanlearntodiscriminatebetweenminesandclutterobjectsaslongastheyhavedi erentsignatures.However,someclutterobjectsmayhaveGPRsignaturesverysimilartominesignatures.Forinstance,a5cmthickmetaldiskwitha30cmdiame-ter,orametalcanmaybeincorrectlyclassiedasmines.Inthiscase,di erentfeaturesandclassiers,orevendi erentsensors,maybeneeded.ACKNOWLEDGMENTSTheworkreportedonherewassupportedinpartbytheUS-Army-Research-O ce-fundedMultidisciplinaryRe-searchonMineDetectionandNeutralizationSystems,Contractno.DAAG55-97-1-0014,andbytheUSArmyGrantnos.DAAB15-01-D-0004andDAAB15-02-D-0003.WethankDr.JamesHarveyandMr.PeteHowardfortheirsupportofthisresearch.Wealsothankthereviewersfortheirconstructivecomments.REFERENCES [1]Landmines,MineActionNewsfromtheUnitedNations,vol.3.2,4thQuarter,1998.[2]HiddenKillers:TheGlobalLandmineCrisis,UnitedStatesDepartmentofStateReport,Publicationno.10575,Septem-ber1998.[3]T.R.Witten,resentstateoftheartinground-penetratingradarsforminedetection,inDetectionandRemediationTechnologiesforMinesandMinelikeTargetsIII,vol.3392ofProceedingsofSPIE,pp.576,Orlando,Fla,USA,April1998. 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1884EURASIPJournalonAppliedSignalProcessing [15]H.Frigui,K.Satyanarayana,andP.D.Gader,Detectionoflandminesusingfuzzyandpossibilisticmembershipfunc-tions,inProc.12thIEEEInternationalConferenceonFuzzySystemsFUZZ,vol.2,pp.834,SaintLouis,Mo,USA,May2003.[16]P.D.Gader,B.N.Nelson,H.Frigui,G.Vaillette,andJ.M.Keller,Fuzzylogicdetectionoflandmineswithgroundpen-etratingradar,SignalProcessing,vol.80,no.6,pp.1069,2000. [17]P.D.Gader,R.Grandhi,W.-H.Lee,J.N.Wislon,andD.K.C.Ho,FeatureanalysisfortheNIITEKground-penetratingradarusingorder-weightedaveragingoperatorsforland-minedetection,inDetectionandRemediationTechnologiesforMinesandMinelikeTargetsIX,vol.5415ofProceedingsofSPIE ,pp.953,Orlando,Fla,USA,April2004.[18]J.G.ProakisandD.G.Manolakis,DigitalSignalProcessing:Principles,AlgorithmsandApplications,Prentice-Hall,Engle-woodCli s,NJ,USA,3rdedition,1996.[19]Y.Zhao,P.D.Gader,P.Chen,andY.Zhang,TrainingDHMMsofmineandcluttertominimizelandminedetec-tionerrors,IEEETrans.Geosci.RemoteSensing,vol.41,no.5,pp.1016,2003.[20]S.MizutaandK.Nakajima,Anoptimaldiscriminativetrain-ingmethodforcontinuousmixturedensityHMMs,inProc.1stInternationalConferenceonSpokenLanguageProcessing(ICSLP,pp.245,Kobe,Japan,November1990.[21]L.R.Rabiner,AtutorialonhiddenMarkovmodelsandse-lectedapplicationsinspeechrecognition,Proc.IEEE,vol.77,no.2,pp.257,1989.[22]G.D.Forney,TheViterbialgorithm,Proc.IEEE,vol.61,no.3,pp.268,1973.[23]L.E.BaumandT.Petrie,Statisticalinferenceforprobabilis-ticfunctionsofnitestateMarkovchains,AnnalsofMathe-maticalStatistics,vol.37,no.6,pp.1554,1966.[24]A.P.Dempster,N.M.Laird,andD.B.Rubin,aximumlikelihoodfromincompletedataviatheEMalgorithm,Jour-naloftheRoyalStatisticalSocietySeriesB,vol.39,no.1,pp.38,1977.[25]L.R.Bahl,P.F.Brown,P.V.deSouza,andR.L.Mer-cer,aximummutualinformationestimationofhiddenMarkovmodelparametersforspeechrecognition,inProc.IEEEInt.Conf.Acoustics,Speech,Signal(ICASSP,pp.52,Tokyo,Japan,April1986.[26]B.Merialdo,PhoneticrecognitionusinghiddenMarkovmodelsandmaximummutualinformationtraining,inProc.IEEEInt.Conf.Acoustics,Speech,Signal(ICASSP,vol.1,pp.111,NewYork,NY,USA,April1988.[27]B.-H.Juang,W.Hou,andC.-H.Lee,Minimumclassica-tionerrorratemethodsforspeechrecognition,IEEETrans.SpeechAudioProcessing,vol.5,no.3,pp.257,1997.[28]S.Katagiri,B.-H.Juang,andC.-H.Lee,atternrecognitionusingafamilyofdesignalgorithmsbaseduponthegeneral-izedprobabilisticdescentmethod,Proc.IEEE,vol.86,no.11,pp.2345,1998.[29]L.R.Bahl,P.F.Brown,P.V.deSouza,andR.L.Mercer,AnewalgorithmfortheestimationofhiddenMarkovmodelparameters,inProc.IEEEInt.Conf.Acoustics,Speech,Signal(ICASSP,vol.1,pp.493,NewYork,NY,USA,April1988. [30]J.R.R.Pressley,D.Pabst,G.D.Sower,L.Nee,B.Green,andP.Howard,Groundstando minedetectionsystem(GSTAMIDS)engineering,manufacturing,anddevelopment(EMD)Block0,inDetectionandRemediationTechnologiesforMinesandMinelikeTargetsVI,vol.4394ofProceedingsofSPIE ,pp.1190,Orlando,Fla,USA,April2001.[31]G.D.Sower,J.Eberly,andE.Christy,GSTAMIDSground-penetratingradar:hardwaredescription,inDetectionandRemediationTechnologiesforMinesandMinelikeTargetsVI, vol.4394ofProceedingsofSPIE,pp.651,Orlando,Fla,USA,April2001.[32]E.G.FarrandC.E.Baum,repulseassociatedwiththeTEMfeedofanimpulseradiatingantenna,SensorandSimulationNote37,AirForceResearchLaboratory,March1992.[33]E.G.Farr,Optimizingthefeedimpedanceofimpulseradiat-ingantennasPartI:ReectorIRAs,SensorandSimulationNote354,AirForceResearchLaboratory,January1993.[34]E.G.FarrandC.J.Buchenauer,ExperimentalvalidationofIRAmodels,SensorandSimulationNote364,AirForceRe-searchLaboratory,January1994.[35]T.Kohonen,mprovedversionsoflearningvectorquantiza-tion,inProc.InternationalJointConferenceonNeuralNet-worksIJCNN,vol.1,pp.545,SanDiego,Calif,USA,June1990.[36]J.R.R.Pressley,D.Pabst,G.D.Sower,L.Nee,B.Green,andP.Howard,Groundstando minedetectionsystem(GSTAMIDS)engineering,manufacturinganddevelopment(EMD)block0,inDetectionandRemediationTechnologiesforMinesandMinelikeTargetsVI,vol.4394ofProceedingsofSPIE ,pp.1190,Orlando,Fla,USA,April2001. HichemFriguiisanAssistantProfessorandtheDirectoroftheMultimediaResearchLab,theUniversityofLouisville,Kentucky.HereceivedhisPh.D.degreeincomputerengineeringandcomputersciencefromtheUniversityofMissouri,Columbia,in1997.From1998to2004,hewasanAssistantPro-fessorattheUniversityofMemphis.Hehasbeenactiveintheresearcheldsofpatternrecognition,datamining,imageprocessing,andcontent-basedimageretrieval.Hehaspublishedover60jour-nalandrefereedconferencearticles,andhasreceivedtheNationalScienceFoundationCareerAwardforoutstandingyoungscientists.Dr.Friguihasbeenactiveinlandminedetectionalgorithmresearchsince1998.Hewasamemberoffewteamsthatdeveloped,imple-mented,andeld-testedseveralreal-timealgorithmsforminede-tectionusinggroundpenetratingradar.Dr.FriguiisaMemberoftheIEEE,IEEEComputerSociety,andACM.Heiscurrentlyserv-ingasanAssociateEditoroftheIEEETransactionsonFuzzySys-tems,andtheInternationalJournalofFuzzySystems. K.C.HowasborninHongKong.Here-ceivedtheB.S.degreewithrst-classhon-oursinelectronicsandthePh.D.degreeinelectronicengineeringfromtheChineseUniversityofHongKong,HongKong,in1988and1991,respectively.HewasaRe-searchAssociateintheRoyalMilitaryCol-legeofCanadafrom1991to1994.HejoinedtheBell-NorthernResearch,Mon-treal,Canada,in1995,asamemberofthescienticsta .HewasafacultymemberattheUniversityofSaskatchewan,Saskatoon,Canada,fromSeptember1996toAu-gust1997.SinceSeptember1997,hehasbeenwiththeUniversityofMissouri,Columbia,whereheiscurrentlyanAssociateProfessorintheElectricalandComputerEngineeringDepartment.Hisresearchinterestsareinstatisticalandadaptivesignalprocessing,sub-surfaceobjectdetection,sourcelocalizations,wavelettransform,andwirelesscommunications.Dr.Hoiscurrentlyservingasan

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Real-TimeLandmineDetectionwithGPRUsingDiscriminativeHMM1885 AssociateEditoroftheIEEETransactionsonSignalProcessing,andtheIEEESignalProcessingLetters.HeisalsotheEditoroftheITU StandardRecommendationG.168:DigitalNetworkEchoCancellers. HehasthreeUSpatents,threeCanadianpatents,andthreeEuro-peanpatentsintheareaofmobilecommunications. PaulGaderreceivedhisPh.D.degreeinmathematicsin1986fromtheUniversityofFlorida.HehasworkedasaSeniorRe-searchScientistatHoneywesSystemsandResearchCenter,asaResearchEngineerandManagerattheEnvironmentalResearchIn-stituteofMichigan,andasafacultymem-berattheUniversityofWisconsin,theUni-versityofMissouri,andtheUniversityofFlorida,whereheiscurrentlyaProfessorofcomputerandinformationscienceandengineering.Heledteamsinvolvedinreal-time,handwrittenaddressrecognitionsystemsfortheUSpostalservicedevelopingalgorithmsforhandwrittendigitrecognitionandsegmentation,numericeldrecognition,wordrecognition,andlinesegmentation.Hehasledteamsthatdevisedandtestedseveralreal-timealgorithmsintheeldforminedetec-tion.HeservedasaTechnicalDirectoroftheUniversityofMissouriMURIonHumanitarianDeminingfortwoyears.Heiscurrentlyinvolvedinlandminedetectionprojectsinvestigatinghandheldandground-baseddetectionsystems,acousticdetection,EO/IRdetec-tionofminesandtrip-wires,hyperspectraldetection,andmulti-sensorfusion.Dr.GaderisaSeniorMemberoftheIEEEandhasover165technicalpublicationsintheareasofimageandsignalpro-cessing,appliedmathematics,andpatternrecognition,includingover50refereedjournalarticles.