SIAM Journal on Scientific and Statistical Computing
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Jacobi Angles for Simultaneous Diagonalization
SIAM Journal on Matrix Analysis and Applications
High-order contrasts for independent component analysis
Neural Computation
Joint Approximate Diagonalization of Positive Definite Hermitian Matrices
SIAM Journal on Matrix Analysis and Applications
Efficient greedy learning of Gaussian mixture models
Neural Computation
Blind Source Separation of Single Components from Linear Mixtures
ICANN '01 Proceedings of the International Conference on Artificial Neural Networks
The Journal of Machine Learning Research
Extraction of Specific Signals with Temporal Structure
Neural Computation
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Joint diagonalization via subspace fitting techniques
ICASSP '01 Proceedings of the Acoustics, Speech, and Signal Processing, 2001. on IEEE International Conference - Volume 05
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
An analytical constant modulus algorithm
IEEE Transactions on Signal Processing
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Nonorthogonal Joint Diagonalization Free of Degenerate Solution
IEEE Transactions on Signal Processing
Blind Separation of Independent Sources Using Gaussian Mixture Model
IEEE Transactions on Signal Processing - Part II
IEEE Transactions on Signal Processing
Blind separation of instantaneous mixtures of nonstationary sources
IEEE Transactions on Signal Processing
Quadratic optimization for simultaneous matrix diagonalization
IEEE Transactions on Signal Processing
Blind source separation based on time-frequency signalrepresentations
IEEE Transactions on Signal Processing
IEEE Transactions on Neural Networks
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In this paper, a new algorithm for approximate joint diagonalization (AJD) of positive-definite Hermitian matrices is presented. The AJD matrix, which is assumed to be square non-unitary, is derived via minimization of a quasi-maximum likelihood (QML) objective function. This objective function coincides asymptotically with the maximum lilelihood (ML) objective function, hence enabling the proposed algorithm to asymptotically approach the ML estimation pllrformance. In the proposed method, the rows of the AJD matrix are obtained independently, in an iterative manner. This featurle enables direct estimation of full row-rank rectangular AJD sub-matrices. Under some mild assumptions, convergence of the proposed algorithm is asymptotically guarantied, such that the error norm corresponding to each row of the AJD matrix reduces significantly after the first iteration, and the convergence is almost Q-super linear. This property results rapid convergence, which leads to low computational load in the proposed method. The performance of the proposed algorithm is evaluated and compared to other state-of-the-art algorithms for AJD and its practical use is demonstrated in the blind source separation and blind source extraction problems. The results imply that under the assumptions of high signal-to-noise ratio and large amount of matrices, the proposed algorithm is computationally efficient with perfonnance similar to state-of-the-art algorithms for AJD.