ROBUST SPARSE RECOVERY FOR COMPRESSIVE SENSING IN IMPULSIVE NOISE USING lP-NORM MODEL FITTING

This work considers the robust sparse recovery problem in compressive sensing (CS) in the presence of impulsive measurement noise. We propose a robust formulation for sparse recovery using the generalized l(p)-norm with 0 < p < 2 as the metric for the residual error under l(1)-norm regularization. An alternative direction method (ADM) has been proposed to solve this formulation efficiently. Moreover, a smoothing strategy has been used to derive a convergent method for the nonconvex case of p < 1. The convergence conditions of the proposed algorithm for both the convex and nonconvex cases have been provided. Numerical simulations demonstrated that the new algorithm can achieve state-of-the-art robust performance in highly impulsive noise.