The minimum entropy and cumulants based contrast functions for blind source extraction

Abstract

In this paper we address the problem of blind source extraction of a subset of "interesting" independent sources from a linear convolutive or instantaneous mixture. The interesting sources are those which are independent and, in a certain sense, are sparse and far away from Gaussianity. We show that in the low-noise limit and when none of the desired sources is Gaussian, the minimum entropy and cumulants based approaches can solve the problem. These criteria, with roots in Blind Deconvolution and in Projection Pursuit, will be proposed here for the simultaneous blind extraction of a group of independent sources. Then, we suggest simple algorithms which, working on the Stiefel manifold perform maximization of the proposed contrast functions. © Springer-Verlag Berlin Heidelberg 2001.