General conditions of stability in blind source separation models and score function selection

This contribution contains a theoretical analysis on asymptotic stability requirements in blind source separation (BSS) algorithms. BSS extracts independent component signals from their mixtures without knowing either the mixing coefficients or the probability distributions of the source signals. It is known that some algorithms work surprisingly well. "blind" means that no a prior information is assumed to be available both on the mixture and on the sources. This feature makes BSS approach versatile because it is not relying on the modeling of some physical phenomena. Nevertheless, few papers mention either convergence or stability of the estimators in the case where one make wrong assumptions on the distribution of the sources. This paper presents and discusses stability conditions for BSS algorithms to avoid spurious stationary points in the case of instantaneous mixtures of independent and identically distributed sources.

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