Approximate Maximum Likelihood Source Separation Using the Natural Gradient

Seungjin Choi, Andrzej Cichocki, Liqing Zhang, Shun-ichi Amari

Abstract: This paper addresses a maximum likelihood method for source separation in the case of overdetermined mixtures corrupted by additive white Gaussian noise. We consider an approximate likelihood which is based on the Laplace approximation and develop a natural gradient adaptation algorithm to find a local maximum of the corresponding approximate likelihood. We present a detailed mathematical derivation of the algorithm using the Lie group invariance. Useful behavior of the algorithm is verified by numerical experiments.