Rank, decomposition, and uniqueness for 3-way and n-way arrays
Multiway data analysis
Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
Jacobi Angles for Simultaneous Diagonalization
SIAM Journal on Matrix Analysis and Applications
A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
Blind separation methods based on Pearson system and its extensions
Signal Processing
Blind identification of under-determined mixtures based on the characteristic function
Signal Processing - Signal processing in UWB communications
SIAM Journal on Matrix Analysis and Applications
On underdetermined source separation
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 03
Enhanced Line Search: A Novel Method to Accelerate PARAFAC
SIAM Journal on Matrix Analysis and Applications
Symmetric Tensors and Symmetric Tensor Rank
SIAM Journal on Matrix Analysis and Applications
Fast algorithms for mutual information based independent component analysis
IEEE Transactions on Signal Processing - Part I
ICAR: a tool for blind source separation using fourth-order statistics only
IEEE Transactions on Signal Processing - Part I
Fourth-order blind identification of underdetermined mixtures of sources (FOBIUM)
IEEE Transactions on Signal Processing
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
On the virtual array concept for the fourth-order direction findingproblem
IEEE Transactions on Signal Processing
On the virtual array concept for higher order array processing
IEEE Transactions on Signal Processing
Algebraic Joint Zero-Diagonalization and Blind Sources Separation
IEEE Transactions on Signal Processing
Blind Identification of Underdetermined Mixtures by Simultaneous Matrix Diagonalization
IEEE Transactions on Signal Processing
Fourth-Order Cumulant-Based Blind Identification of Underdetermined Mixtures
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Parallel factor analysis in sensor array processing
IEEE Transactions on Signal Processing
Independent component analysis and (simultaneous) third-ordertensor diagonalization
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Positive definite combination of symmetric matrices
IEEE Transactions on Signal Processing
Blind identification and source separation in 2×3 under-determined mixtures
IEEE Transactions on Signal Processing
A generalization of joint-diagonalization criteria for sourceseparation
IEEE Transactions on Signal Processing
Blind source separation for ambulatory sleep recording
IEEE Transactions on Information Technology in Biomedicine
Cumulant-based independence measures for linear mixtures
IEEE Transactions on Information Theory
Complex random vectors and ICA models: identifiability, uniqueness, and separability
IEEE Transactions on Information Theory
Joint eigenvalue decomposition using polar matrix factorization
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
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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.