Jacobi Angles for Simultaneous Diagonalization
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
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
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
Blind Signal Separation Using Steepest Descent Method
IEEE Transactions on Signal Processing
Algebraic Joint Zero-Diagonalization and Blind Sources Separation
IEEE Transactions on Signal Processing
Adaptive subspace algorithm for blind separation of independentsources in convolutive mixture
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Quadratic optimization for simultaneous matrix diagonalization
IEEE Transactions on Signal Processing
A generalization of joint-diagonalization criteria for sourceseparation
IEEE Transactions on Signal Processing
Iterative Algorithm for Joint Zero Diagonalization With Application in Blind Source Separation
IEEE Transactions on Neural Networks
A Fast Algorithm for Nonunitary Joint Diagonalization and Its Application to Blind Source Separation
IEEE Transactions on Signal Processing
A Direct Algorithm for Nonorthogonal Approximate Joint Diagonalization
IEEE Transactions on Signal Processing
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This paper addresses the problem of joint block diagonalization (JBD) of a set of given matrices. As is known that the nonunitary JBD algorithm has some advantages over the existing orthogonal one for convolutive blind source separation (CBSS). However, the nonunitary JBD algorithm is prone to converge to some unexpected degenerate solutions (singular or ill-conditioned solutions). Especially for the matrices of large dimension or the case that the number of the diagonal blocks is relatively large, the performances of the nonunitary JBD algorithm degrade more severely. To eliminate the degenerate solutions, we optimize a penalty term based weighted least-squares criterion and thus develop a fast efficient algorithm. The performance of the proposed algorithm is evaluated by computer simulations and compared with the existing state-of-the-art nonunitary JBD algorithm. The simulation results demonstrate the robustness and performance improvement of the proposed algorithm.