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

Abstract

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

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.