Robust blind source separation algorithms using cumulants

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In this paper we propose a new approach to blind separation of independent source signals that, while avoiding the imposition of an orthogonal mixing matrix, is robust with respect to the existence of additive Gaussian noise in the mixture. We demonstrate that, for the wide class of source distributions with certain non-null cumulants and a pre-specified scaling, separation is always a saddle point of a cumulant-based cost function. We propose a quasi-Newton approach for determining this saddle point. This enables us to obtain a family of separation algorithms which, based on higher order statistics, yields unbiased estimates even in the presence of large Gaussian noise and has the interesting property of local isotropic convergence. Another family of algorithms that incorporates second-order statistics loses the former desirable convergence properties but it provides more precise estimates in the absence of noise. Extensive computer simulations confirm robustness and the excellent performance of the resulting algorithms.