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Recently, the $\l_{p}$-norm regularization minimization problem$(P_{p}^{\lambda})$ has attracted great attention in compressed sensing.However, the $\l_{p}$-norm $\|x\|_{p}^{p}$ in problem $(P_{p}^{\lambda})$ isnonconvex and non-Lipschitz for all $p\in(0,1)$, and there are not manyoptimization theories and methods are proposed to solve this problem. In fact,it is NP-hard for all $p\in(0,1)$ and $\lambda>0$. In this paper, we study twomodified $\l_{p}$ regularization minimization problems to approximate theNP-hard problem $(P_{p}^{\lambda})$. Inspired by the good performance of Halfalgorithm and $2/3$ algorithm in some sparse signal recovery problems, twoiterative thresholding algorithms are proposed to solve the problems$(P_{p,1/2,\epsilon}^{\lambda})$ and $(P_{p,2/3,\epsilon}^{\lambda})$respectively. Numerical results show that our algorithms perform effectively infinding the sparse signal in some sparse signal recovery problems for someproper $p\in(0,1)$.

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