A New Link Between Joint Blind Source Separation Using Second Order Statistics and the Canonical Polyadic Decomposition

Dana Lahat 1, 2, 3 Chrisitan Jutten 1
1 GIPSA-VIBS - VIBS
GIPSA-DIS - Département Images et Signal
2 CNRS - Centre National de la Recherche Scientifique
3 IRIT - Institut de recherche en informatique de Toulouse
Abstract : In this paper, we discuss the joint blind source separation (JBSS) of real-valued Gaussian stationary sources with uncorrelated samples from a new perspective. We show that the second-order statistics of the observations can be reformulated as a coupled decomposition of several tensors. The canonical polyadic decomposition (CPD) of each such tensor, if unique, results in the identification of one or two mixing matrices. The proposed new formulation implies that standard algorithms for joint diagonalization and CPD may be used to estimate the mixing matrices, although only in a sub-optimal manner. We discuss the uniqueness and identifiability of this new approach. We demonstrate how the proposed approach can bring new insights on the uniqueness of JBSS in the presence of underdetermined mixtures.
Keywords : identifiability uniqueness Joint blind source separation independent vector analysis tensor canonical polyadic decomposition
Type de document :
Communication dans un congrès
Deville Y., Gannot S., Mason R., Plumbley M., Ward D. Latent Variable Analysis and Signal Separation, Jul 2018, Guildford, United Kingdom. 10891, pp.171--180, 2018, Lecture Notes in Computer Science
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https://hal.archives-ouvertes.fr/hal-01884793
Contributeur : Dana Lahat <>
Soumis le : lundi 1 octobre 2018 - 13:34:46
Dernière modification le : jeudi 11 octobre 2018 - 13:29:30

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Dana Lahat, Chrisitan Jutten. A New Link Between Joint Blind Source Separation Using Second Order Statistics and the Canonical Polyadic Decomposition. Deville Y., Gannot S., Mason R., Plumbley M., Ward D. Latent Variable Analysis and Signal Separation, Jul 2018, Guildford, United Kingdom. 10891, pp.171--180, 2018, Lecture Notes in Computer Science. 〈hal-01884793〉

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