Joint Approximate Diagonalization of Positive Definite Hermitian Matrices
SIAM Journal on Matrix Analysis and Applications
The Journal of Machine Learning Research
Joint diagonalization via subspace fitting techniques
ICASSP '01 Proceedings of the Acoustics, Speech, and Signal Processing, 2001. on IEEE International Conference - Volume 05
Joint anti-diagonalization for blind source separation
ICASSP '01 Proceedings of the Acoustics, Speech, and Signal Processing, 2001. on IEEE International Conference - Volume 05
Permutation correction in the frequency domain in blind separation of speech mixtures
EURASIP Journal on Applied Signal Processing
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
Algebraic Joint Zero-Diagonalization and Blind Sources Separation
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Wigner distribution of noisy signals
IEEE Transactions on Signal Processing
Equivariant adaptive source separation
IEEE Transactions on Signal Processing
Complex-Valued Matrix Differentiation: Techniques and Key Results
IEEE Transactions on Signal Processing
Blind source separation based on time-frequency signalrepresentations
IEEE Transactions on Signal Processing
A generalization of joint-diagonalization criteria for sourceseparation
IEEE Transactions on Signal Processing
Computing the polyadic decomposition of nonnegative third order tensors
Signal Processing
Joint block diagonalization algorithms for optimal separation of multidimensional components
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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This article addresses the problem of the non-unitary joint block diagonalization of a given set of complex matrices. Two new algorithms are provided: the first is based on a classical gradient approach and the second is based on a relative gradient approach. For each algorithm, two versions are provided: the fixed stepsize and the optimal stepsize version. Computer simulations are provided to illustrate the behavior of both algorithms in different contexts. Finally, it is shown that these algorithms enable solving the problem of the blind separation of finite impulse response (FIR) convolutive mixtures of (non-stationary correlated) sources. We focus on methods based on the use of spatial quadratic time-frequency spectra or distributions. The suggested approach main advantage is to enable the elimination of the spatial whitening of the observations which has been proven to establish a bound with regard to the best reachable performances in the blind sources separation context.