Abstract:

Recently, the l p minimization problem (p ∈ (0, 1)) for sparse signal recovery has been studied a lot because of its efficiency. In this paper, we propose a general smoothing algorithmic framework based on the entropy function for solving a class of l _p minimization problems, which includes the well-known unconstrained l₂–l _p problem as a special case.We show that any accumulation point of the sequence generated by the proposed algorithm is a stationary point of the l p minimization problem, and derive a lower bound for the nonzero entries of the stationary point of the smoothing problem. We implement a specific version of the proposed algorithm which indicates that the entropy function-based algorithm is effective.

Key words: l _p minimization problem ·, Entropy function ·, Smoothing conjugate gradient method