Maximum Correntropy Adaptive Filtering Approach for Robust Compressive Sensing Reconstruction

TL;DR

This paper introduces a novel adaptive filtering algorithm based on maximum correntropy for robust compressive sensing reconstruction, effectively handling non-Gaussian noise and improving performance over existing methods.

Contribution

It proposes the $l_0$-MCC algorithm combining adaptive filtering and maximum correntropy, with theoretical stability analysis and a mini-batch variant for faster convergence.

Findings

Outperforms existing robust CS algorithms in simulations

Demonstrates robustness to impulsive non-Gaussian noise

Achieves better reconstruction accuracy and convergence speed

Abstract

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