Methods for ℓp/TVp Regularized Optimization and Their Applications in Sparse Signal Processing
| dc.contributor.author | Yan, Jie | |
| dc.contributor.supervisor | Lu, Wu-Sheng | |
| dc.date.accessioned | 2014-11-14T16:11:22Z | |
| dc.date.available | 2014-11-14T16:11:22Z | |
| dc.date.copyright | 2014 | en_US |
| dc.date.issued | 2014-11-14 | |
| dc.degree.department | Department of Electrical and Computer Engineering | |
| dc.degree.level | Doctor of Philosophy Ph.D. | en_US |
| dc.description.abstract | Exploiting signal sparsity has recently received considerable attention in a variety of areas including signal and image processing, compressive sensing, machine learning and so on. Many of these applications involve optimization models that are regularized by certain sparsity-promoting metrics. Two most popular regularizers are based on the l1 norm that approximates sparsity of vectorized signals and the total variation (TV) norm that serves as a measure of gradient sparsity of an image. Nevertheless, the l1 and TV terms are merely two representative measures of sparsity. To explore the matter of sparsity further, in this thesis we investigate relaxations of the regularizers to nonconvex terms such as lp and TVp "norms" with 0 <= p < 1. The contributions of the thesis are two-fold. First, several methods to approach globally optimal solutions of related nonconvex problems for improved signal/image reconstruction quality have been proposed. Most algorithms studied in the thesis fall into the category of iterative reweighting schemes for which nonconvex problems are reduced to a series of convex sub-problems. In this regard, the second main contribution of this thesis has to do with complexity improvement of the l1/TV-regularized methodology for which accelerated algorithms are developed. Along with these investigations, new techniques are proposed to address practical implementation issues. These include the development of an lp-related solver that is easily parallelizable, and a matrix-based analysis that facilitates implementation for TV-related optimizations. Computer simulations are presented to demonstrate merits of the proposed models and algorithms as well as their applications for solving general linear inverse problems in the area of signal and image denoising, signal sparse representation, compressive sensing, and compressive imaging. | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.bibliographicCitation | J. Yan and W.-S. Lu. “Compressive imaging by generalized total variation minimization.” IEEE Asia Pacific Conference on Circuits & Systems, to be held in Okinawa, Japan. Nov. 2014. | en_US |
| dc.identifier.bibliographicCitation | J. Yan and W.-S. Lu. “Image denoising by generalized total variation regularization and least squares fidelity.” Multidimensional Systems and Signal Processing 2013, Springer US. DOI 10.1007/s11045-013-0255-2. | en_US |
| dc.identifier.bibliographicCitation | J. Yan and W.-S. Lu. “Fast dual-based linearized Bregman algorithm for compressive sensing of digital images.” IASTED International Conference on Visualization, Imaging and Image Processing, Banff, AB, Canada. July 2012. | en_US |
| dc.identifier.bibliographicCitation | J. Yan and W.-S. Lu. “Smoothed ℓp-ℓ2 solvers for signal denoising.” IEEE International Conference on Acoustics, Speech, and Signal Processing, Kyoto, Japan. Mar. 2012. | en_US |
| dc.identifier.bibliographicCitation | J. Yan and W.-S. Lu. “Power-iterative strategy for ℓp-ℓ2 optimization for compressive sensing: towards global solution.” Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, United States. Nov. 2011. | en_US |
| dc.identifier.bibliographicCitation | J. Yan and W.-S. Lu. “New algorithms for sparse representation of discrete signals based on ℓp-ℓ2 optimization.” IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, Victoria, BC, Canada. Aug. 2011. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/5728 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights.temp | Available to the World Wide Web | en_US |
| dc.subject | Iteratively Reweighted ℓ1-minimization (IRL1) | en_US |
| dc.subject | Iteratively Reweighted Total Variation (IRTV) | en_US |
| dc.subject | Linearized Bregman (LB) | en_US |
| dc.subject | Magnetic Resonance Imaging (MRI) | en_US |
| dc.subject | Weighted Total Variation (WTV) | en_US |
| dc.subject | Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) | en_US |
| dc.subject | Total Variation (TV) | en_US |
| dc.subject | Fast Gradient Projection (FGP) | en_US |
| dc.subject | Compressive Imaging (CI) | en_US |
| dc.subject | Compressive Sensing (CS) | en_US |
| dc.subject | Basis Pursuit (BP) | en_US |
| dc.title | Methods for ℓp/TVp Regularized Optimization and Their Applications in Sparse Signal Processing | en_US |
| dc.type | Thesis | en_US |