Astrophysical image separation by blind time--frequency source separation methods
Digital Signal Processing
Least Square Joint Diagonalization of Matrices under an Intrinsic Scale Constraint
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Fast approximate joint diagonalization incorporating weight matrices
IEEE Transactions on Signal Processing
Nonorthogonal approximate joint diagonalization with well-conditioned diagonalizers
IEEE Transactions on Neural Networks
Multidimensional Systems and Signal Processing
IEEE Transactions on Signal Processing
Complex independent component analysis by entropy bound minimization
IEEE Transactions on Circuits and Systems Part I: Regular Papers
QML-based joint diagonalization of positive-definite hermitian matrices
IEEE Transactions on Signal Processing
Independent component analysis by entropy bound minimization
IEEE Transactions on Signal Processing
Nonorthogonal independent vector analysis using multivariate Gaussian model
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Complex non-orthogonal joint diagonalization based on LU and LQ decompositions
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
On computation of approximate joint block-diagonalization using ordinary AJD
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
A parallel dual matrix method for blind signal separation
Neural Computation
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The problem of approximate joint diagonalization of a set of matrices is instrumental in numerous statistical signal processing applications. For nonorthogonal joint diagonalization based on the weighted least-squares (WLS) criterion, the trivial (zero) solution can simply be avoided by adopting some constraint on the diagonalizing matrix or penalty terms. However, the resultant algorithms may converge to some undesired degenerate solutions (nonzero but singular or ill-conditioned solutions). This paper discusses and analyzes the problem of degenerate solutions in detail. To solve this problem, a novel nonleast-squares criterion for approximate nonorthogonal joint diagonalization is proposed and an efficient algorithm, called fast approximate joint diagonalization (FAJD), is developed. As compared with the existing nonorthogonal diagonalization algorithms, the new algorithm can not only avoid the trivial solution but also any degenerate solutions. Theoretical analysis shows that the FAJD algorithm has some advantages over the existing nonorthogonal diagonalization algorithms. Simulation results are presented to demonstrate the efficiency of this paper's algorithm