Blind underdetermined mixture identification by joint canonical decomposition of HO cumulants

Ahmad Karfoul (1) , Laurent Albera (2) , Gwénaël Birot (2)

1 Faculty of Mechanical and Electrical Engineering [Homs]
2 LTSI - Laboratoire Traitement du Signal et de l'Image

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.

Mots clés: BSS; ICA; INDSCAL; PARAFAC; Blind underdetermined mixture identification (BUMI); Canonical decomposition; Underdetermined mixture

Domaines: Analyse numérique [math.NA]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Machine Learning [stat.ML]

Ahmad Karfoul, Laurent Albera, Gwénaël Birot. Blind underdetermined mixture identification by joint canonical decomposition of HO cumulants. IEEE Transactions on Signal Processing, 2010, 58 (2), pp.638-649. ⟨10.1109/TSP.2009.2031731⟩. ⟨hal-00593307⟩