  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 $(P_{p}^{\lambda})$ 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 $\lambda>0$. In this paper, we study two
modified $\l_{p}$ regularization minimization problems to approximate the
NP-hard problem $(P_{p}^{\lambda})$. 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
$(P_{p,1/2,\epsilon}^{\lambda})$ and $(P_{p,2/3,\epsilon}^{\lambda})$
respectively. Numerical results show that our algorithms perform effectively in
finding the sparse signal in some sparse signal recovery problems for some
proper $p\in(0,1)$.
