On a new blind signal extraction algorithm: different criteria and stability analysis

In this letter, we consider the problem of simultaneous blind signal extraction of arbitrary group sources from a rather large number of observations. Amari (2000) proposed a gradient algorithm that optimizes the maximum-likelihood (ML) criteria on the Stiefel manifold and solves the problem when the approximate (or hypothetical) densities of the desired signals are a priori known. This letter shows how to extend this result to other contrast functions that do not require explicit knowledge of the sources densities. We also present the algorithm necessary and sufficient local stability conditions, providing useful bounds for the learning step size.