Optimization of a second-order statistics blind separation algorithm for Gaussian signals

The Second-Order Blind Identification (SOBI) algorithm (Belouchrani et al., 1997) is aimed at blind separation of static mixtures of stationary source signals with distinct spectra. It uses approximate joint diagonalization of empirical correlation matrices to estimate the mixing matrix. We show that SOBI's performance can be improved by transforming the joint diagonalization into a properly weighted nonlinear Least Squares problem. In the case of Gaussian sources, the optimal weights can be estimated consistently from the empirical correlation matrices. We demonstrate the substantial improvement by analysis and simulations.