Volume 28, Issue 2
Fixed-Point Continuation Applied to Compressed Sensing: Implementation and Numerical Experiments

J. Comp. Math., 28 (2010), pp. 170-194.

Published online: 2010-04

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• Abstract

Fixed-point continuation (FPC) is an approach, based on operator-splitting and continuation, for solving minimization problems with $\ell_1$-regularization: \min \|x\|_1 + \bar{\mu} f(x). We investigate the application of this algorithm to compressed sensing signal recovery, in which $f(x) = \frac{1}{2}\|Ax-b\|_M^2$, $A \in \R^{m \times n}$ 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.

• Keywords

$\ell_1$ regularization Fixed-point algorithm

65K05 90C06 90C25 90C90.

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• TXT
@Article{JCM-28-170, author = {Elaine T. Hale Wotao Yin and Yin Zhang}, title = {Fixed-Point Continuation Applied to Compressed Sensing: Implementation and Numerical Experiments}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {2}, pages = {170--194}, abstract = {

Fixed-point continuation (FPC) is an approach, based on operator-splitting and continuation, for solving minimization problems with $\ell_1$-regularization: \min \|x\|_1 + \bar{\mu} f(x). We investigate the application of this algorithm to compressed sensing signal recovery, in which $f(x) = \frac{1}{2}\|Ax-b\|_M^2$, $A \in \R^{m \times n}$ 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.10-m1007}, url = {http://global-sci.org/intro/article_detail/jcm/8514.html} }
TY - JOUR T1 - Fixed-Point Continuation Applied to Compressed Sensing: Implementation and Numerical Experiments AU - Elaine T. Hale Wotao Yin & Yin Zhang JO - Journal of Computational Mathematics VL - 2 SP - 170 EP - 194 PY - 2010 DA - 2010/04 SN - 28 DO - http://dor.org/10.4208/jcm.2009.10-m1007 UR - https://global-sci.org/intro/article_detail/jcm/8514.html KW - $\ell_1$ regularization KW - Fixed-point algorithm KW - AB -

Fixed-point continuation (FPC) is an approach, based on operator-splitting and continuation, for solving minimization problems with $\ell_1$-regularization: \min \|x\|_1 + \bar{\mu} f(x). We investigate the application of this algorithm to compressed sensing signal recovery, in which $f(x) = \frac{1}{2}\|Ax-b\|_M^2$, $A \in \R^{m \times n}$ 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.

Elaine T. Hale Wotao Yin & Yin Zhang. (1970). Fixed-Point Continuation Applied to Compressed Sensing: Implementation and Numerical Experiments. Journal of Computational Mathematics. 28 (2). 170-194. doi:10.4208/jcm.2009.10-m1007
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