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

Abstract Recently, the l p -norm regularization minimization problem ( P p λ ) has attracted great attention in compressed sensing. However, the l p -norm ‖x‖ p p in problem ( P p λ ) 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 ) and λ > 0 . In this paper, we study one modified l p -norm regularization minimization problem to approximate the NP-hard problem ( P p λ ) . 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 , ϵ λ ) . 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.