Inertial iterative thresholding with applications to sparse and low-rank signal recovery

Johnstone, Patrick

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https://hdl.handle.net/2142/50628 Copy

Description

Title

Inertial iterative thresholding with applications to sparse and low-rank signal recovery

Author(s)

Johnstone, Patrick

Issue Date

2014-09-16

Director of Research (if dissertation) or Advisor (if thesis)

Moulin, Pierre

Department of Study

Electrical & Computer Eng

Discipline

Electrical & Computer Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Date of Ingest

2014-09-16T17:24:31Z

Keyword(s)

• Iterative shrinkage and thresholding
• gradient descent with momentum
• the heavy-ball method
• the conjugate gradient method

Abstract

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.

Graduation Semester

2014-08

Permalink

http://hdl.handle.net/2142/50628

Copyright and License Information

2014 Patrick Royce Johnstone

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