Information theoretic learning for inverse problem resolution in bio-electromagnetism

Abstract

This paper addresses the issue of learning directly from the observed data in Blind Source Separation (BSS), a particular inverse problem. This problem is very likely to occur when we are dealing with two or more independent electromagnetic sources. A powerful approach to BSS is Independent Component Analysis (ICA). This approach is much more powerful if no apriori assumption about data distribution is made: this is possible transferring as much information as possible to the learning machine defining a cost function based on an information theoretic criterion. In particular, Renyi's definition of entropy and mutual information are introduced and MERMAID (Minimum Renyi's Mutual Information), an algorithm for ICA based on such these definitions, is here described, implemented and tested over a popular BSS problem in bio-electromagnetism: fetal Electrocardiogram (fECG) extraction. MERMAID was compared to the well known algorithm INFOMAX and it showed to better learn from data and to provide a better source separation. The extracted fECG signals were finally postprocessed by wavelet analysis. © Springer-Verlag Berlin Heidelberg 2007.