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

  • Dana LahatEmail author
  • Christian Jutten
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10891)


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.


Joint blind source separation Independent vector analysis Tensor Canonical polyadic decomposition Uniqueness Identifiability 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-labGrenobleFrance

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