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Sparse and redundant representations...

Patel, Vishal M.

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Sparse and redundant representations for inverse problems and recognition.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Sparse and redundant representations for inverse problems and recognition./
Author:	Patel, Vishal M.
Description:	150 p.
Notes:	Source: Dissertation Abstracts International, Volume: 71-11, Section: B, page: .
Contained By:	Dissertation Abstracts International71-11B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3426406
ISBN:	9781124270647

Sparse and redundant representations for inverse problems and recognition.
Patel, Vishal M.

Sparse and redundant representations for inverse problems and recognition. - 150 p.

Source: Dissertation Abstracts International, Volume: 71-11, Section: B, page: .

Thesis (Ph.D.)--University of Maryland, College Park, 2010.

Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertation, we study applications of sparse and redundant representations in inverse problems and object recognition. Furthermore, we propose two novel imaging modalities based on the recently introduced theory of Compressed Sensing (CS).

ISBN: 9781124270647Subjects--Topical Terms:

1669109
Applied Mathematics.

Sparse and redundant representations for inverse problems and recognition.
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020 $a 9781124270647
035 $a (UMI)AAI3426406
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040 $a UMI $c UMI
100 1 $a Patel, Vishal M. $3 1672502
245 1 0 $a Sparse and redundant representations for inverse problems and recognition.
300 $a 150 p.
500 $a Source: Dissertation Abstracts International, Volume: 71-11, Section: B, page: .
500 $a Adviser: Rama Chellappa.
502 $a Thesis (Ph.D.)--University of Maryland, College Park, 2010.
520 $a Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertation, we study applications of sparse and redundant representations in inverse problems and object recognition. Furthermore, we propose two novel imaging modalities based on the recently introduced theory of Compressed Sensing (CS).
520 $a This dissertation consists of four major parts. In the first part of the dissertation, we study a new type of deconvolution algorithm that is based on estimating the image from a shearlet decomposition. Shearlets provide a multi-directional and multi-scale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. We develop a deconvolution algorithm that allows for the approximation inversion operator to be controlled on a multi-scale and multi-directional basis. Furthermore, we develop a method for the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation method.
520 $a In the second part of the dissertation, we study a reconstruction method that recovers highly undersampled images assumed to have a sparse representation in a gradient domain by using partial measurement samples that are collected in the Fourier domain. Our method makes use of a robust generalized Poisson solver that greatly aids in achieving a significantly improved performance over similar proposed methods. We will demonstrate by experiments that this new technique is more flexible to work with either random or restricted sampling scenarios better than its competitors.
520 $a In the third part of the dissertation, we introduce a novel Synthetic Aperture Radar (SAR) imaging modality which can provide a high resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. We demonstrate that this new imaging scheme, requires no new hardware components and allows the aperture to be compressed. Also, it presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements.
520 $a The last part of the dissertation deals with object recognition based on learning dictionaries for simultaneous sparse signal approximations and feature extraction. A dictionary is learned for each object class based on given training examples which minimize the representation error with a sparseness constraint. A novel test image is then projected onto the span of the atoms in each learned dictionary. The residual vectors along with the coefficients are then used for recognition. Applications to illumination robust face recognition and automatic target recognition are presented.
590 $a School code: 0117.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Engineering, Electronics and Electrical. $3 626636
650 4 $a Remote Sensing. $3 1018559
690 $a 0364
690 $a 0544
690 $a 0799
710 2 $a University of Maryland, College Park. $b Electrical Engineering. $3 1018746
773 0 $t Dissertation Abstracts International $g 71-11B.
790 1 0 $a Chellappa, Rama, $e advisor
790 1 0 $a Chellappa, Rama $e committee member
790 1 0 $a Duraiswami, Ramani $e committee member
790 1 0 $a Wu, Min $e committee member
790 1 0 $a Liu, K. J. Ray $e committee member
790 1 0 $a Benedetto, John J. $e committee member
790 1 0 $a Easley, Glenn R. $e committee member
790 $a 0117
791 $a Ph.D.
792 $a 2010
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3426406