Fixed-Point Continuation Applied to Compressed Sensing: Implementation and Numerical Experiments

Fixed-Point Continuation Applied to Compressed Sensing: Implementation and Numerical Experiments

Year:    2010

Author:    Elaine T. Hale, Wotao Yin, Yin Zhang

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 2 : pp. 170–194

Abstract

Fixed-point continuation (FPC) is an approach, based on operator-splitting and continuation, for solving minimization problems with $\ell_1$-regularization:

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We investigate the application of this algorithm to compressed sensing signal recovery, in which $f(x) = \frac{1}{2}\|Ax-b\|_M^2$, $A \in \mathbb{R}^{m \times n}$ and $m \leq n$.  In particular, we extend the original algorithm to obtain better practical results, derive appropriate choices for $M$ and $\bar{\mu}$ under a given measurement model, and present numerical results for a variety of compressed sensing problems. The numerical results show that the performance of our algorithm compares favorably with that of several recently proposed algorithms.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2009.10-m1007

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 2 : pp. 170–194

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    $\ell_1$ regularization Fixed-point algorithm Continuation Compressed sensing Numerical experiments.

Author Details

Elaine T. Hale

Wotao Yin

Yin Zhang