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 joint diagonalization by combining givens and hyperbolic rotations
IEEE Transactions on Signal Processing
Nonorthogonal approximate joint diagonalization with well-conditioned diagonalizers
IEEE Transactions on Neural Networks
On blind separability based on the temporal predictability method
Neural Computation
Multidimensional Systems and Signal Processing
Convolutive blind speech separation by decorrelation
ICONIP'08 Proceedings of the 15th international conference on Advances in neuro-information processing - Volume Part I
Convolutive blind source separation by fourth-order statistics
ICICS'09 Proceedings of the 7th international conference on Information, communications and signal processing
QML-based joint diagonalization of positive-definite hermitian matrices
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
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
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Simultaneous diagonalization of a set of matrices is a technique that has numerous applications in statistical signal processing and multivariate statistics. Although objective functions in a least-squares sense can be easily formulated, their minimization is not trivial, because constraints and fourth-order terms are usually involved. Most known optimization algorithms are, therefore, subject to certain restrictions on the class of problems: orthogonal transformations, sets of symmetric, Hermitian or positive definite matrices, to name a few. In this paper, we present a new algorithm called QDIAG that splits the overall optimization problem into a sequence of simpler second order subproblems. There are no restrictions imposed on the transformation matrix, which may be nonorthogonal, indefinite, or even rectangular, and there are no restrictions regarding the symmetry and definiteness of the matrices to be diagonalized, except for one of them. We apply the new method to second-order blind source separation and show that the algorithm converges fast and reliably. It allows for an implementation with a complexity independent of the number of matrices and, therefore, is particularly suitable for problems dealing with large sets of matrices