An Infimal Convolution based Penalty for Sparse Signal Recovery

Abstract

In this paper, we propose a nonconvex penalty function for sparse signal recovery by using infimal convolution approximation. First, we show that this penalty function is between the l 1 -norm and the difference of l 1 and l 2 -norm (l 1 2- norm), thus it can retain the advantages of these two norms at the same time, which means that it can induce the sparsity effectively for the low-amplitude components as the l 1 -norm and relieve underestimating the high-amplitude components as the l 1 2 -norm. Second, we present an iterative method to solve the nonconvex penalty minimization based on the difference of convex algorithm (DCA), which solves the subproblem by using alternating direction method of multipliers (ADMM) method. The experimental results demonstrate the effectiveness of the proposed method.