Maximum correntropy adaptation approach for robust compressive sensing reconstruction

Robust compressive sensing (CS) aims to recover the sparse signals from noisy measurements perturbed by non-Gaussian (i.e., heavy-tailed) noises, where traditional CS reconstruction algorithms may perform poorly owing to utilizing the l₂ error norm in optimization. In this paper, we propose a novel maximum correntropy adaptation approach for robust CS reconstruction. The task is formulated as a l₀ regularized maximum correntropy criterion (l₀-MCC) optimization problem and is solved by adaptive filtering approach. The proposed l₀-MCC algorithm has a simple algorithm structure and can adaptively estimate the sparsity. It can efficiently alleviate the negative impact of noise in the presence of large outliers. Moreover, a novel theoretical analysis on convergence of l₀-MCC is also performed. Furthermore, a mini-batch-based l₀-MCC (MB-l₀-MCC) algorithm is developed to speed up the convergence. Comparison with existing robust CS reconstruction algorithms is conducted via simulations, showing that the proposed methods can achieve better performance than existing state-of-the-art algorithms.