Impulsive Noise Robust Sparse Recovery via Continuous Mixed Norm

TL;DR

This paper introduces a novel robust sparse recovery method using Continuous Mixed Norm (CMN) to handle impulsive noise modeled by stable distributions, improving recovery accuracy in unknown noise conditions.

Contribution

It proposes a new CMN-based approach for robust sparse recovery that outperforms existing methods, especially when noise parameters are unknown.

Findings

CMN improves robustness against impulsive noise.

The method outperforms recent algorithms in simulations.

ADMM and Majorization-Minimization facilitate efficient optimization.

Abstract

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 $S\alpha S$ distribution, alternative approximations like Generalized Gaussian Distribution (GGD) are used which impose $\ell_p$-norm fidelity on the residual error. In this paper, we exploit a Continuous Mixed Norm (CMN) for robust sparse recovery instead of $\ell_p$-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.