Iterative thresholding algorithm based on non-convex method for modified lp-norm regularization minimization

Recently, the l(p)-norm regularization minimization problem (P-p(lambda)) has attracted great attention in compressed sensing. However, the l(p)-norm parallel to x parallel to(p)(p) in problem (P-p(lambda)) is nonconvex and non-Lipschitz for all p is an element of (0, 1), and there are not many optimization theories and methods proposed to solve this problem. In fact, it is NP-hard for all p is an element of (0, 1) and lambda > 0. In this paper, we study one modified 1 p -norm regularization minimization problem to approximate the NP-hard problem (P-p(lambda)). Inspired by the good performance of Half algorithm in some sparse signal recovery problems, an iterative thresholding algorithm is proposed to solve our modified l(p)-norm regularization minimization problem (P-P,1/2 epsilon(lambda))d Numerical results on some sparse signal recovery problems show that our algorithm performs effectively in finding the sparse signals compared with some state-of-art methods. (C) 2018 Elsevier B.V. All rights reserved.