Overcomplete Independent Component Analysis via Linearly Constrained Minimum Variance Spatial Filtering

Authors:
Moritz Grosse-Wentrup;Martin Buss
Affiliations:
Institute of Automatic Control Engineering, Technische Universität München, München, Germany 80290;Institute of Automatic Control Engineering, Technische Universität München, München, Germany 80290
Venue:
Journal of VLSI Signal Processing Systems
Year:
2007

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Abstract

Independent Component Analysis (ICA) designed for complete bases is used in a variety of applications with great success, despite the often questionable assumption of having N sensors and M sources with N驴M. In this article, we assume a source model with more sources than sensors (MN), only LN of which are assumed to have a non-Gaussian distribution. We argue that this is a realistic source model for a variety of applications, and prove that for ICA algorithms designed for complete bases (i.e., algorithms assuming N=M) based on mutual information the mixture coefficients of the L non-Gaussian sources can be reconstructed in spite of the overcomplete mixture model. Further, it is shown that the reconstructed temporal activity of non-Gaussian sources is arbitrarily mixed with Gaussian sources. To obtain estimates of the temporal activity of the non-Gaussian sources, we use the correctly reconstructed mixture coefficients in conjunction with linearly constrained minimum variance spatial filtering. This results in estimates of the non-Gaussian sources minimizing the variance of the interference of other sources. The approach is applied to the denoising of Event Related Fields recorded by MEG, and it is shown that it performs superiorly to ordinary ICA.