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

Recently, the lp-norm regularization minimization problem (Ppλ) has attracted great attention in compressed sensing. However, the lp-norm ‖x‖pp in problem (Ppλ) is nonconvex and non-Lipschitz for all p∈(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∈(0,1) andλ>0. In this paper, we study one modified lp-norm regularization minimization problem to approximate the NP-hard problem (Ppλ). Inspired by the good performance of Half algorithm in some sparse signal recovery problems, an iterative thresholding algorithm is proposed to solve our modified lp-norm regularization minimization problem (Pp,1∕2,ϵλ). 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.