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Robust compressive sensing(CS) reconstruction has become an attractiveresearch topic in recent years. Robust CS aims to reconstruct the sparsesignals under non-Gaussian(i.e. heavy tailed) noises where traditional CSreconstruction algorithms may perform very poorly due to utilizing $l_2$ normof the residual vector in optimization. Most of existing robust CSreconstruction algorithms are based on greedy pursuit method or convexrelaxation approach. Recently, the adaptive filtering framework has beenintroduced to deal with the CS reconstruction, which shows desirableperformance in both efficiency and reconstruction performance under Gaussiannoise. In this paper, we propose an adaptive filtering based robust CSreconstruction algorithm, called $l_0$ regularized maximum correntropycriterion($l_0$-MCC) algorithm, which combines the adaptive filtering frameworkand maximum correntropy criterion(MCC). MCC has recently been successfully usedin adaptive filtering due to its robustness to impulsive non-Gaussian noisesand low computational complexity. We analyze theoretically the stability of theproposed $l_0$-MCC algorithm. A mini-batch based $l_0$-MCC(MB-$l_0$-MCC)algorithm is further developed to speed up the convergence. Comparison withexisting robust CS reconstruction algorithms is conducted via simulations,showing that the proposed $l_0$-MCC and MB-$l_0$-MCC can achieve significantlybetter performance than other algorithms.

Maximum Correntropy Adaptive Filtering Approach for Robust Compressive Sensing Reconstruction