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 (BSS) has to deal with statistically dependent signals. ► Nonnegative signals are efficiently separated by dedicated BSS methods. ► We propose a new algorithm which is based on convex geometry considerations. ► Our algorithm was successfully applied to NMR and EEG one-dimensional signals and to images.