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 L₁ 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 L₁ regularization, the hard-threshold filtering for L₀ 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.