Volumetric Data Reconstruction from Irregular Samples and Compressively Sensed Measurements

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Material Information

Title:
Volumetric Data Reconstruction from Irregular Samples and Compressively Sensed Measurements
Physical Description:
1 online resource (115 p.)
Language:
english
Creator:
Xu, Xie
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Computer Engineering, Computer and Information Science and Engineering
Committee Chair:
ENTEZARI,ALIREZA
Committee Co-Chair:
VEMURI,BABA C
Committee Members:
RANGARAJAN,ANAND
BANERJEE,ARUNAVA
PAUL,ANAND ABRAHAM

Subjects

Subjects / Keywords:
box-splines -- compressed-sensing -- reconstruction -- sampling -- sparse-approximation -- sparse-representation -- volumetric-data
Computer and Information Science and Engineering -- Dissertations, Academic -- UF
Genre:
Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
Sampling and reconstruction of volumetric data are ubiquitous throughout biomedical imaging, scientific simulation, and visualization applications. In this dissertation, we focus on the reconstruction of volumetric data from irregular samples as well as compressively sensed measurements. We examine different sampling lattices and their respective shift-invariant spaces for the reconstruction of irregularly sampled volumetric data. Given an irregularly sampled dataset, we demonstrate that the non-tensor-product approximations corresponding to the Body Centered Cubic (BCC) lattice and the Face Centered Cubic (FCC) lattice provide more accurate reconstructions than the tensor-product approximations associated with the commonly-used Cartesian lattice. Our study is motivated by the sampling-theoretic advantages of the BCC lattice and the FCC lattice over the Cartesian lattice. Our practical algorithm utilizes multidimensional box spline functions and $\sinc$ functions that are tailored to these lattices. We also present a regularization scheme that provides a variational reconstruction framework for efficient implementation. The improvements in accuracy are quantified numerically and visualized in our experiments with synthetic as well as real biomedical datasets. We also examine compressed sensing principles for the sparse approximation of volumetric datasets. We propose that the compressed sensing framework can be used for a refinable and reusable data reduction framework for the in-situ processing of volumetric datasets. Instead of saving a high resolution dataset, only a few partial Fourier measurements of the original dataset are kept for data reduction. These measurements are sensed without any prior knowledge of specific feature domains for the dataset. The original dataset can be recovered from the saved measurements. We demonstrate the superiority of the analysis recovery model along with surfacelets for efficient representation of volumetric data. We establish that the accuracy of reconstruction can further improve when the basis for sparser representations of data becomes available. To facilitate our study, we also construct a novel non-separable 3-D tight wavelet frame decomposition using a seven direction box spline for sparse representation of the data. Our studies and experiment results motivate future research on the study of custom-designed sparse representations for large-scale volumetric data.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Xie Xu.
Thesis:
Thesis (Ph.D.)--University of Florida, 2014.
Local:
Adviser: ENTEZARI,ALIREZA.
Local:
Co-adviser: VEMURI,BABA C.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2016-05-31

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2014
System ID:
UFE0046527:00001