A Robust Iteratively Reweighted $\ell _2$ Approach for Spectral Compressed Sensing in Impulsive Noise

Abstract

This letter concentrates on the problem of spectral compressed sensing in impulsive noise, which aims to recover a spectrally sparse signal from its contaminated and undersampled measurements. We propose a robust formulation for joint sparse signal and frequency recovery, which includes the generalized $\ell _p$ -norm $(0 data-fidelity fitting term added to a log-sum sparsity-promoting regularizer. To handle this intractable issue, we develop an iteratively reweighted $\ell _2$ approach via majorizing the original objective function by a quadratic surrogate function. Simulation results illustrate that the proposed approach attains a significant performance improvement over the existing methods under impulsive noise.