Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 58, Issue 2, Pages 638-649Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2009.2031731
Keywords
BSS; blind underdetermined mixture identification (BUMI); canonical decomposition; ICA; INDSCAL; PARAFAC; underdetermined mixture
Categories
Funding
- French Government
- ANR DECOTES [06-BLAN-0074]
- mv-EMD [BLAN07-0314-02]
- ACOMB-SOLARE
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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.
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