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

Elaine T. Hale Wotao Yin and Yin Zhang

10.4208/jcm.2009.10-m1007

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

Full Article 1 26
  • 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.

  • History

Published online: 2010-04

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