Analytical Solution of the Blind Source Separation Problem Using Derivatives

In this paper, we consider independence property between a random process and its first derivative. Then, for linear mixtures, we show that cross-correlations between mixtures and their derivatives provide a sufficient number of equations for analytically computing the unknown mixing matrix. In addition to its simplicity, the method is able to separate Gaussian sources, since it only requires second order statistics. For two mixtures of two sources, the analytical solution is given, and a few experiments show the efficiency of the method for the blind separation of two Gaussian sources.

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