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

• Published in: Journal of computational and applied mathematics Vol. 347; pp. 173 - 180
• Main Authors: Cui, Angang, Peng, Jigen, Li, Haiyang, Wen, Meng, Jia, Junxiong
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2019
• Subjects: [formula omitted] algorithm; [formula omitted]-norm; Compressed sensing; Modified [formula omitted]-norm; 49M20; lp-norm; 65K10; 1∕2−ϵ algorithm; 90C26; Compressed sensing; Modified lp-norm
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2018.08.021

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.