A Non-convex Optimization Model for Signal Recovery

Abstract

The electroencephalogram (EEG) signal is one of the most frequently used biomedical signals. In order to accurately exploit the cosparsity and low-rank property which is nature in multichannel EEG signals, motivated by the fact that weighted schatten-p norm and $${l_q}$$ norm can better approximate the matrix rank and $${l_0}$$ norm, in this paper, a non-convex optimization model is proposed to precisely reconstruct the multichannel EEG signal. weighted schatten-p norm and $${l_q}$$ norm are used to enforce low-rank property and cosparsity. In addition, an efficient iterative optimization method based on alternating direction method of multipliers is used to solve the resulting non-convex optimization problem. Experimental results have demonstrated that the proposed algorithm can significantly outperform existing state-of-the-art CS methods for compressive sensing of multichannel EEG signals.