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”. In many real-world cases, however, source signals are considerably dependent. In order to cope with such signals, we proposed in [1] a geometric method that separates dependent signals provided that they are nonnegative and locally orthogonal. This paper also presents a geometric method for separating nonnegative source signals which relies on an assumption weaker than local orthogonality. The separation problem relies on the identification of relevant facets of the data cone. After a rigorous proof of the proposed method, we give the details of the separation algorithm and report experiments carried out on signals from various origins, clearly showing the contribution of our method.