A unifying criterion for blind source separation and decorrelation: Simultaneous diagonalization of correlation matrices

Blind source separation and blind output decorrelation are two well-known problems in signal processing. For instantaneous mixtures, blind source separation is equivalent to a generalized eigen-decomposition, while blind output decorrelation can be considered as an iterative method of output orthogonalization. We propose a steepest descent procedure on a new cost function based on the Frobenius norm which measures the diagonalization of correlation matrices to perform blind source separation as well as blind decorrelation. The method is applicable to both stationary and nonstationary signals and instantaneous as well as convolutive mixture models. Simulation results by Monte Carlo trials are provided to show the consistent performance of the proposed algorithm.