Generic blind source separation using second-order local statistics

Exploiting the fact that one is dealing with time signals, it is possible to formulate certain blind source (or signal) separation tasks in terms of a simple generalized eigenvalue decomposition based on two matrices. Many of the techniques determine these two matrices using second-order statistics, e.g., variance, covariance, autocorrelation, etc. In this work, we present a second-order, covariance-based method to determine the independent components of a linear mixture of sources. This is accomplished without the use of a possible temporal variable on which the data may depend, i.e., we explicitly avoid the use of autocorrelations, time delay, etc. in our formulation. The latter makes it possible to apply the simple eigenvalue decomposition-based technique to general pattern recognition methods and as such to find possible independent components of generic point clouds.