2026-09-20T16:46:13Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/50628 2023-07-11 col_2142_5131 col_2142_8888 com_2142_5130 com_2142_8887 com_2142_234

en Moulin, Pierre Johnstone, Patrick 2014-09-16T17:24:31Z 2014-09-16T17:24:31Z 2014-08 2014-09-16 2014-08 This thesis is concerned with a class of methods known collectively as iterative thresholding algorithms. These methods have been used by researchers for several decades to solve various optimization problems that arise in signal processing, inverse problems, pattern recognition and other related fields. One such problem of great interest is compressed sensing, where the goal is to recover a signal that is known to be sparse from fewer linear measurements than the dimension of the signal. Another is low-rank matrix completion where one wants to recover a low-rank matrix from a subset of revealed entries. A third example is robust principle component analysis (RPCA) where one is given a data matrix and would like to decompose it into a low-rank component and a sparse component. Other examples include total variation denoising and deblurring, and L`1-regularized regression. Iterative thresholding methods have low complexity, but they typically take many iterations to converge, especially on ill-conditioned problems. In this thesis we explore how inertia can be used to accelerate iterative thresholding algorithms. A second problem with iterative thresholding algorithms is they tend to become trapped in undesirable local minima when the problem is non-convex. We discuss how inertia can help iterative thresholding methods to avoid local minima and propose several schemes to solve well-known non-convex problems. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2014-07-18T20:16:22Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Johnstone_Patrick.pdf: 455974 bytes, checksum: 867544a79b251a823d525364201f6409 (MD5) Made available in DSpace on 2014-09-16T17:24:31Z (GMT). No. of bitstreams: 2 Patrick_Johnstone.pdf: 455974 bytes, checksum: 867544a79b251a823d525364201f6409 (MD5) license.txt: 4067 bytes, checksum: 3fe5774af723481022579fc9b5d37a44 (MD5) http://hdl.handle.net/2142/50628 2014 Patrick Royce Johnstone Iterative shrinkage and thresholding gradient descent with momentum the heavy-ball method the conjugate gradient method Inertial iterative thresholding with applications to sparse and low-rank signal recovery text Electrical & Computer Eng 1933 Electrical & Computer Engr 1200 University of Illinois at Urbana-Champaign Thesis M.S. MS:Electr & Computer Eng-UIUC 10KS1200MS