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 l1-regularization: min||x||1 +μf(x). We investigate the application of this algorithm to compressed sensing signal recovery, in which f(x) = 1/2||Ax-b||M2, A∈ℝm×n and m ≤ n. In particular, we extend the original algorithm to obtain better practical results, derive appropriate choices for M and μ 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. © 2010 by AMSS, Chinese Academy of Sciences.