Blind source separation via symmetric eigenvalue decomposition

We propose a new sufficient condition for separation of colored source signals with temporal structure, stating that the separation is possible, if the source signals have different higher self-correlation functions of even order. 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 depending on -dimensional parameter , if this matrix has distinct eigenvalues. We prove that the parameters for which this is possible, form an open subset of , which complement has a Lebesgue measure zero. We use a robust orthogonalization of the mixing matrix, which is not sensitive to the white noise, and propose a new sufficient condition for that: the source signals to have linearly independent higher self-correlation functions of even order. We propose a new one-step algorithm, based on the non-smooth optimization theory, which disperses the eigenvalues of the matrix providing sufficient distance between them.