A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
Blind source separation of positive and partially correlated data
Signal Processing
A convex analysis-based minimum-volume enclosing simplex algorithm for hyperspectral unmixing
IEEE Transactions on Signal Processing
Blind separation of instantaneous mixtures of dependent sources
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
A Convex Analysis Framework for Blind Separation of Non-Negative Sources
IEEE Transactions on Signal Processing - Part II
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
A geometric approach to multiple-channel signal detection
IEEE Transactions on Signal Processing
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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.