Robust compressive sensing of multichannel EEG signals in the presence of impulsive noise

Latest studies have shown that combining cosparsity and low-rank property usually results in efficient compressive sensing (CS) recovery approaches for multichannel electroencephalogram (EEG) signals. However, existing methods rarely consider noise or consider only the influence of Gaussian noise generated during transmission. When the measurement is corrupted by impulsive noise, the performance of these CS approaches will degrade. In this study, a new robust CS approach is proposed to accurately recover multichannel EEG signals from noisy measurements in the presence of impulsive noise. We first employ Welsch estimator to depress the influence of impulsive noise in CS reconstruction. We further develop an efficient iterative scheme based on half-quadratic theory and alternating direction method of multipliers to solve the resulting nonconvex optimization problem. Experimental results show that our approach can obtain better reconstruction results than those of existing state-of-the-art CS methods when measurements are corrupted by impulsive noise.