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.

This paper presents novel techniques for blind separation and blind extraction of instantaneously mixed binary sources, which are suitable for the case with less sensors than sources. First, a solvability analysis is presented for a general case. Necessary and sufficient conditions for recoverability of all or some part of sources are derived. A new deterministic blind separation algorithm is then proposed to estimate the mixing matrix and separate all sources efficiently in the noise-free or low noise level case. Next, using the Maximum Likelihood (ML) approach for robust estimation of centers of clusters, we have extended the algorithm for high additive noise case. Moreover, a new sequential blind extraction algorithm has been developed, which enables us not only to extract the potentially separable sources but also estimate their number. The sources can be extracted in a specific order according to their dominance (strength) in the mixtures. At last, simulation results are presented to illustrate the validity and high performance of the algorithms.