Proximal methods for reweighted lQ-regularization of sparse signal recovery

摘要

To recover a sparse signal from a noised linear measurement system Ax=b+e, convex lp regularization methods (i.e., 1 ≤ p < 2, in particular, 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, in particular, 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.