Blind separation methods based on Pearson system and its extensions

Abstract

We introduce a mutual information-based method for blind separation of statistically independent source signals. The Pearson system is used as a parametric model. Starting from the definition of mutual information we show using the results by Pham (IEEE Trans. Signal Process. 44(11) (1996) 2768–2779) that the minimization of mutual information contrast leads to iterative use of score functions as estimation functions. The Pearson system allows adaptive modeling of the score functions. The characteristics of the Pearson system are studied and estimators for the parameters are derived using the method of moments. The flexibility of the Pearson system makes it possible to model wide range of source distributions including asymmetric distributions. Skewed source distributions are common in many key application areas, such as telecommunications and biomedical signal processing. We also introduce an extension of the Pearson system that can model multimodal distributions. The applicability of the Pearson system-based method is demonstrated in simulation examples, including blind equalization of GMSK signals.