Robust blind source separation and dispersing algorithms

We show that statistically independent source signals can be separated simultaneously, if for some time delays p they have nonzero cumulants cu(si) (p) = cu{s(i) (k), s(i) (k), s(i) (k - p), s(i) (k - p)}. If the sources have distinct cumulant functions, then the separation is possible with another procedure, which could be more effective for large scale problems. In both cases the problem of blind source separation can be converted to a symmetric eigenvalue problem of a generalized cumulant matrices, which are not sensitive to Gaussian noise. We propose new algorithms, based on the non-smooth optimization theory, which disperse the eigenvalues of these generalized cumulant matrices. We propose new orthogonalization procedure for the mixing matrix, which is robust to additive Gaussian noise.