Dynamic signal mixtures and blind source separation

Methods for blind source separation (BSS) from linear instantaneous signal mixtures have drawn a significant attention due to their ability to recover original independent non-Gaussian sources without analyzing their temporal statistics. Hence, original voices or images (module permutation and linear scaling) are extracted from their mixtures without modeling the dynamics of the signals. The typical methods for performing blind source separation are linear independent component analysis (ICA) and the infomax method. Linear ICA directly penalizes a suitably chosen measure of the statistical dependence between the extracted signals. These measures are either obtained from the information theoretic postulates such as the mutual information or from the cumulant expansion of the associated probability density functions. The infomax method is based on the entropy maximization of the non-linear transformation of the separated signals. This paper analyzes extensions of the instantaneous blind source separation techniques to the case of linear dynamic signal mixtures. Furthermore, the paper introduces a novel method based on combining time delayed decorrelation (TDD) with the minimization of the cumulant cost function. TDD is used to obtain an acceptable initial condition for the cumulant based cost function optimization in order to reduce the numerical complexity of the latter method. This combined approach is illustrated on two examples including a real life cocktail party example.