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
Joint eigenvalue decomposition using polar matrix factorization
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Simple LU and QR based non-orthogonal matrix joint diagonalization
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
Nonorthogonal Joint Diagonalization Free of Degenerate Solution
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
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In this paper, we propose a class of complex non-orthogonal joint diagonalization (NOJD) algorithms with successive rotations. The proposed methods consider LU or LQ decompositions of the mixing matrices, and propose to solve the NOJD problem via two successive stages: L-stage and U (or Q)-stage. Moreover, as the manifolds of target matrices in these stages could be appropriately parameterized by a sequence of simple elementary triangular or unitary matrices, which depend on only one or two parameters, the high-dimensional minimization problems could be replaced by a sequence of lower-dimensional ones. As such, the proposed algorithms are of simple closed-form in each iteration, and do not require the target matrices to be Hermitian nor positive definite. Simulations are provided to compare the proposed methods to other complex NOJD methods.