Robust maximum signal fraction analysis for blind source separation

Blind source separation (BSS) is an active research topic in the fields of biomedical signal processing and brain-computer interface. As a representative technique, maximum signal fraction analysis (MSFA) has been recently developed for the problem of BSS. However, MSFA is formulated based on the L2-norm, and thus is prone to be negatively affected by outliers. In this study, the authors propose a robust alternative to MSFA based on the L1-norm, termed as MSFA-L1. Specifically, they re-define the objective function of MSFA, in which the energy quantities of both the signal and the noise are defined with the L1-norm rather than the L2-norm. By adopting the L1-norm, MSFA-L1 alleviates the negative influence of large deviations that are usually associated with outliers. Computationally, they design an iterative algorithm to optimise the objective function of MSFA-L1. The iterative procedure is shown to converge under the framework of bound optimisation. Experimental results on both synthetic data and real biomedical data demonstrate the effectiveness of the proposed MSFA-L1 approach.