Characteristic-function-based independent component analysis
Signal Processing - Special section: Security of data hiding technologies
The Journal of Machine Learning Research
Reference-based blind source separation using a deflation approach
Signal Processing
A zero-cumulant random variable and its applications
Signal Processing - Special section: Distributed source coding
Blind separation of any source distributions via high-order statistics
Signal Processing
Blind source separation using Wold decomposition and second order statistics
MATH'05 Proceedings of the 7th WSEAS International Conference on Applied Mathematics
Blind source separation based on cumulants with time and frequency non-properties
IEEE Transactions on Audio, Speech, and Language Processing
Nonorthogonal approximate joint diagonalization with well-conditioned diagonalizers
IEEE Transactions on Neural Networks
Blind underdetermined mixture identification by joint canonical decomposition of HO cumulants
IEEE Transactions on Signal Processing
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
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
A general algebraic algorithm for blind extraction of one source in a MIMO convolutive mixture
IEEE Transactions on Signal Processing
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In the field of blind source separation, joint-diagonalization-based approaches constitute an important framework, leading to useful algorithms such as the popular joint approximate diagonalization of eigenmatrices (JADE) and simultaneous third-order tensor diagonalization (STOTD) algorithms. However, they are often restricted to the case of cumulants of order four. In this paper, we extend the results leading to JADE and STOTD to cumulants of any order greater than or equal to three by exhibiting a new family of contrast functions that constitutes then a unified framework for the above known results. This also leads us to generalize some links between contrast functions and joint-diagonalization criteria on which these algorithms are based. In turn, one contrast of the new family allows us to show that a function previously proposed as a separation criterion is also a contrast. Moreover, for the two generalized JADE and STOTD contrasts, the analytical optimal solution in the case of two sources is derived and shown to keep the same simple expression, whatever the cumulant order. Finally, some computer simulations illustrate the potential advantage one can take by considering statistics of different orders for the joint-diagonalization of cumulant matrices