Separation of statistically dependent sources using an L2L2-distance non-Gaussianity measure

We provide a solution to the BSS problem for the special case of statistically dependent sources. We propose the MaxNG algorithm based on the maximization of a non-Gaussianity (NG) measure which is equivalent to minimizing the Shannon entropy of source estimates. We compare our algorithm against a strategy commonly used which is based on the minimization of mutual information (MinMI). It is shown that, for uncorrelated sources, both strategies arrive at similar solutions but when sources are dependent (correlated), better results are obtained using MaxNG. In order to measure NG, we use a non-parametric density estimation technique, namely Parzen windows, and L2L2-Euclidean distance in the space of density functions. A wide set of simulations based on real world data with complex dependence structures is presented, showing that our MaxNG algorithm successfully separates the sources, even when the original sources are strongly dependent for which traditional MinMI algorithms, such as ICA, usually fail. Many experimental results are provided to evaluate the performance of our algorithm for two and six sources. Comparisons of MaxNG with some popular BSS algorithms are provided. The main conclusion of the present work is that, our NG measure provides a useful tool for separating dependent signals since original sources usually represent local maxima of this measure.