Blind separation of mixture of independent sources through a quasi-maximum likelihood approach

We propose two methods for separating mixture of independent sources without any precise knowledge of their probability distribution. They are obtained by considering a maximum likelihood (ML) solution corresponding to some given distributions of the sources and relaxing this assumption afterward. The first method is specially adapted to temporally independent non-Gaussian sources and is based on the use of nonlinear separating functions. The second method is specially adapted to correlated sources with distinct spectra and is based on the use of linear separating filters. A theoretical analysis of the performance of the methods has been made. A simple procedure for optimally choosing the separating functions is proposed. Further, in the second method, a simple implementation based on the simultaneous diagonalization of two symmetric matrices is provided. Finally, some numerical and simulation results are given, illustrating the performance of the method and the good agreement between the experiments and the theory.