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

Elaine T. Hale, Wotao Yin & Yin Zhang

DOI: 10.4208/jcm.2009.10-m1007

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:

image.png


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.

  • Keywords

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

  • AMS Subject Headings

65K05, 90C06, 90C25, 90C90

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-170, author = {Hale , Elaine T.Yin , Wotao and Zhang , Yin}, 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:

image.png


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.

}, 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 - Hale , Elaine T. AU - Yin , Wotao AU - Zhang , Yin JO - Journal of Computational Mathematics VL - 2 SP - 170 EP - 194 PY - 2010 DA - 2010/04 SN - 28 DO - http://doi.org/10.4208/jcm.2009.10-m1007 UR - https://global-sci.org/intro/article_detail/jcm/8514.html KW - $\ell_1$ regularization, Fixed-point algorithm, Continuation, Compressed sensing, Numerical experiments. AB -

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

image.png


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.

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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