The role of whitening for separation of synchronous sources

Abstract

The separation of synchronous sources (SSS) is a relevant problem in the analysis of electroencephalogram (EEG) and magnetoencephalogram (MEG) synchrony. Previous experimental results, using pseudo-real MEG data, showed empirically that prewhitening improves the conditioning of the SSS problem. Simulations with synthetic data also suggest that the mixing matrix is much better conditioned after whitening is performed. Unlike in Independent Component Analysis (ICA), synchronous sources can be correlated. Thus, the reasoning used to motivate whitening in ICA is not directly extendable to SSS. In this paper, we analytically derive a tight upper bound for the condition number of the equivalent mixing matrix after whitening. We also present examples with simulated data, showing the correctness of this bound on sources with sub- and super-gaussian amplitudes. These examples further illustrate the large improvements in the condition number of the mixing matrix obtained through prewhitening, thus motivating the use of prewhitening in real applications. © 2012 Springer-Verlag.