Impulsive Noise Robust Sparse Recovery via Continuous Mixed Norm
This work addresses robust sparse recovery for signal processing applications in noisy environments, representing an incremental improvement over existing methods.
The paper tackles sparse signal recovery in the presence of additive impulsive noise by using a Continuous Mixed Norm (CMN) instead of traditional ℓp-norm methods, achieving near-optimal recovery in blind conditions where noise parameters are unknown, with simulation results confirming its efficiency compared to recent algorithms.
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 $SαS$ 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.