Iterative thresholding algorithm based on non-convex method for modified lp-norm regularization minimization
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 $p\in(0,1)$.