A Lorentzian-[formula omitted] norm regularization based algorithm for recovering sparse signals in two types of impulsive noise

Abstract

In this paper, we present a Lorentzian-ℓp(0<p<1) optimization for recovering sparse signals from measurements corrupted by two types of impulsive noise. A smoothing strategy for nonconvex ℓp norm is employed and an efficient Lorentzian based iterative algorithm is developed for solving the resulting optimization problem. We describe the detailed process of the algorithm and establish the convergence of the proposed algorithm. Numerical results show that our proposed algorithm performs effectively in recovering sparse signals from impulsive measurement noise compared with the state-of-the-art methods.