A robust iteratively reweighted l₂ approach for spectral compressed sensing in impulsive noise

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 l_p - norm (0 < p < 2) data-fidelity fitting term added to a log-sum sparsity-promoting regularizer. To handle this intractable issue, we develop an iteratively reweighted l₂ 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.