Iterative thresholding algorithm based on non-convex method for modified lp-norm regularization minimization - Cui, Angang; Peng, Jigen; Li, Haiyang; Wen, Meng; Xiong, Jiajun (2018)
Recently, the$ł_{p}$ -norm regularization minimization problem$(P_{p}^{λ})$has attracted great attention in compressed sensing. However, the$ł_{p}$ -norm$\|x\|_{p}^{p}$in problem$(P_{p}^{λ})$is nonconvex and non-Lipschitz for all$p\in(0,1)$ , and there are not many optimization theories and methods are proposed to solve this problem. In fact, it is NP-hard for all$p\in(0,1)$and$λ>0$ . In this paper, we study two modified$ł_{p}$regularization minimization problems to approximate the NP-hard problem$(P_{p}^{λ})$ . Inspired by the good performance of Half algorithm and$2/3$algorithm in some sparse signal recovery problems, two iterative thresholding algorithms are proposed to solve the problems$(P_{p,1/2,ε}^{λ})$and$(P_{p,2/3,ε}^{λ})$respectively. Numerical results show that our algorithms perform effectively in finding the sparse signal in some sparse signal recovery problems for some proper$p\in(0,1)$ .