General thresholding representation for the Lp regularization problem

Inspired by the Compressive sensing (CS) theory, the L
_p
regularization methods have attracted a great attention. The L
_p
regularization is a generalized version of the well-known L
₁
regularization for sparser solution. In this paper, we derive a general thresholding representation for the L
_p
(0 <; p <; 1) regularization problem in term of a recursive function, which can be well approximated by few steps. This representation can be simplified to the well-known soft-threshold filtering for L
₁
regularization, the hard-threshold filtering for L
₀
regularization, and the recently reported half-threshold filtering for L
_1/2
regularization. This general threshold representation can be easily incorporated into the iterative thresholding framework to provide a tool for sparsity problems.