Criteria for the Simultaneous Blind Extraction of Arbitrary Groups of Sources

This paper reviews several existing contrast functions for blind source extraction proposed in the areas of Projection Pursuit and Independent Component Analysis, in order to extend them to allow the simultaneous blind extraction of an arbitrary number of sources which is specified by user. Using these criteria a novel form of Amari’s extraction algorithm has been derived. The necessary and sufficient asymptotical stability conditions that we obtain for this algorithm help us to develop step-sizes that result in a fast convergence. Finally, we exhibit some exemplary simulations that validate our theoretical results and illustrate the excellent performance of the presented algorithms.