Astrophysical image separation by blind time--frequency source separation methods
Digital 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
Multidimensional Systems and Signal Processing
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Non unitary joint block diagonalization of complex matrices using a gradient approach
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
QML-based joint diagonalization of positive-definite hermitian matrices
IEEE Transactions on Signal Processing
Blind source separation based on high-resolution time-frequency distributions
Computers and Electrical Engineering
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This paper deals with the blind separation of instantaneous mixtures of source signals using time-frequency distributions (TFDs). We propose iterative algorithms to perform the nonorthogonal zero diagonalization and/or joint diagonalization of given sets of matrices. As an application, we show that the source separation can be realized by applying one of these algorithms to a set of spatial quadratic TFD matrices corresponding only to the so-called cross-source terms and/or to the so-called autosource terms. The determination of the above matrices to be jointly decomposed requires first an automatic selection procedure of useful time-frequency points. Regarding this last point, we also propose a new selection procedure and a modification of an existing one and provide a comparison with other existing ones. The nonorthogonal joint diagonalization and/or zero diagonalization algorithm's main advantage is to not require (in the blind source separation context) a prewhitening stage, which allows them to work even with a class of correlated signals and provides generally improved separation performance. Finally, an analytical example and computer simulations are provided in order to illustrate the effectiveness of the proposed approach and to compare it with classical ones