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An Iterative Method Using Conditional Second-Order Statistics Applied to the Blind Source Separation Problem

Abstract : This paper is concerned with the problem of blind separation of instantaneous mixture of sources (BSS) which has been addressed in many ways. When power spectral densities of the sources are different, methods using second-order statistics are sufficient to solve this problem. Otherwise these methods fail and others (higher-order statistics,...) must be used. In this paper, we propose an iterative method to process the case of sources with the same power spectral density. This method is based on an evaluation of conditional first and second-order statistics only. Restrictions on characteristics of sources are given to reach a solution, and proofs of convergence of the algorithm are provided for particular cases of probability density functions. Robustness of this algorithm with respect to the number of sources is shown through computer simulations. A particular case of sources which have a probability density function with unbounded domain of definition is described; here the algorithm does not lead directly to a separation state, but to an a priori known mixture state. Finally, prospects of links with contrast functions are mentioned, with a possible generalization of them based on results obtained with particular sources.
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Bernard Xerri, Bruno Borloz. An Iterative Method Using Conditional Second-Order Statistics Applied to the Blind Source Separation Problem. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2004, 52 (2), pp.313-328. ⟨10.1109/TSP.2003.820986⟩. ⟨hal-01823752⟩

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