Blind source separation via symmetric eigenvalue decomposition
Pando Georgiev, Andrzej S Cichocki · 2002
We propose a sufficient condition for separation of colored source signals with temporal structure, stating that the separation is possible, if the source signals have different auto-correlation functions. We show that the problem of blind source separation of uncorrelated colored signals can be converted to a symmetric eigenvalue problem of a special covariance matrix Z(b)=/spl Sigma//sub i=1//sup L/b(p/sub i/)R/sub z/(p/sub i/) depending on L-dimensional parameter b, if this matrix has distinct eigenvalues. We prove that the parameters b for which this is possible, form an open subset of R/sup L/, whose complement has a Lebesgue measure zero. A robust orthogonalization of the mixing matrix is used, which is not sensitive to the white noise. We propose a new one-step algorithm, based on non-smooth optimization theory, which disperses the eigenvalues of the matrix Z(b) providing sufficient distance between them.