Proximal methods for reweighted l-regularization of sparse signal recovery

Abstract

Abstract To recover a sparse signal from a noised linear measurement system A x = b + e , convex lp regularization methods (i.e., 1 ≤ p p = 1 ) are commonly used under certain conditions. Recently, however, more attentions have been paid to nonconvex lq regularization methods (i.e., 0 q = 1 / 2 ) for recovering a sparse signal. In this paper, we use proximal methods to study both convex and nonconvex reweighted lQ regularization for recovering a sparse signal. Convex lQ regularization is introduced by S. Voronin and I. Daubechies [19]. We extend it to the nonconvex case and our results therefore supplement those of Voronin and Daubechies [19] . We also study Nesterov’s acceleration method for the nonconvex case. Our numerical experiments show that nonconvex lQ regularization can more effectively recover sparse signals.