A geometric approach to blind separation of nonnegative and dependent source signals
Blind source separation (BSS) consists in processing a set of observed mixed signals to separate them into a set of original components. Most of the current blind separation methods assumes that the source signals are as statistically independent as possible given the observed data. In many real-world situations, however, this hypothesis does not hold. In order to cope with such signals, a first geometric method was proposed that separates statistically dependent signals, provided that they are nonnegative and locally orthogonal. This paper presents a new geometric method for the separation of nonnegative source signals which relies on a working assumption that is weaker than local orthogonality. The separation problem is expressed as the identification of relevant facets of the data cone. After a rigorous proof of the proposed method, the details of the separation algorithm are given. Experiments on signals from various origins clearly show the efficiency of the new procedure.
blind source separation dependent signals convex geometry facet identification dual cone