Eigenvalue problem approach to the blind source separation: Optimization with a reference signal

Abstract

The eigenvalue problem approach to the blind source separation [L. Molgedey and H. G. Schuster, Phys. Rev. Lett. 72, 3634 (1994)] is reinvestigated. The essential assumption is that the source signals should be statistically independent for the eigenvalue method to be applicable. When the source signals are correlated, unfortunately, this elegant approach faces a serious problem of optimization. We propose that by employing a reference signal in the separation procedure, the reconstructed signals that have an optimum minimum mismatch to the original sources can be obtained. The role and the criterion in choosing the reference signal will be extensively illustrated. Furthermore, the influences of nonzero correlation between different source signals, finite data length, and channel noises on signal separation will also be fully clarified.