1 research outputs found
Impulsive Noise Robust Sparse Recovery via Continuous Mixed Norm
This paper investigates the problem of sparse signal recovery in the presence
of additive impulsive noise. The heavytailed impulsive noise is well modelled
with stable distributions. Since there is no explicit formulation for the
probability density function of distribution, alternative
approximations like Generalized Gaussian Distribution (GGD) are used which
impose -norm fidelity on the residual error. In this paper, we exploit
a Continuous Mixed Norm (CMN) for robust sparse recovery instead of
-norm. We show that in blind conditions, i.e., in case where the
parameters of noise distribution are unknown, incorporating CMN can lead to
near optimal recovery. We apply Alternating Direction Method of Multipliers
(ADMM) for solving the problem induced by utilizing CMN for robust sparse
recovery. In this approach, CMN is replaced with a surrogate function and
Majorization-Minimization technique is incorporated to solve the problem.
Simulation results confirm the efficiency of the proposed method compared to
some recent algorithms in the literature for impulsive noise robust sparse
recovery