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Blind Underdetermined Mixture Identification by Joint Canonical Decomposition of HO Cumulants

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3 Author(s)
Karfoul, A. ; LTSI, Univ. de Rennes 1, Rennes, France ; Albera, L. ; Birot, G.

A new family of cumulant-based algorithms is proposed in order to blindly identify potentially underdetermined mixtures of statistically independent sources. These algorithms perform a joint canonical decomposition (CAND) of several higher order cumulants through a CAND of a three-way array with special symmetries. These techniques are studied in terms of identifiability, performance and numerical complexity. From a signal processing viewpoint, the proposed methods are shown i) to have a better estimation resolution and ii) to be able to process more sources than the other classical cumulant-based techniques. Second, from a numerical analysis viewpoint, we deal with the convergence speed of several procedures for three-way array decomposition, such as the ACDC scheme. We also show how to accelerate the iterative CAND algorithms by using differently the symmetries of the considered three-way array. Next, from a multilinear algebra viewpoint the paper aims at giving some insights on the uniqueness of a joint CAND of several Hermitian multiway arrays compared to the CAND of only one array. This allows us, as a result, to extend the concept of virtual array (VA) to the case of combination of several VAs.

Published in:

Signal Processing, IEEE Transactions on  (Volume:58 ,  Issue: 2 )

Date of Publication:

Feb. 2010

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