General thresholding representation for the Lp regularization problem

Abstract

Inspired by the Compressive sensing (CS) theory, the Lp regularization methods have attracted a great attention. The Lp regularization is a generalized version of the well-known L1 regularization for sparser solution. In this paper, we derive a general thresholding representation for the Lp (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 L1 regularization, the hard-threshold filtering for L0 regularization, and the recently reported half-threshold filtering for L1/2 regularization. This general threshold representation can be easily incorporated into the iterative thresholding framework to provide a tool for sparsity problems.