An Adaptive Nonunitary Joint Diagonalization Algorithm of High-Order Tensors

A new algorithm to solve the fused complex-valued cost function for approximate joint diagonalization (AJD), named CVAJD (Complex-Valued Approximate Joint Diagonalization), is presented. The CVAJD algorithm adopts an iterative scheme to update the demixing matrix through the strictly diagonally-dominant residual mixing matrix obtained in each of iterations. Due to the relaxation of several constraints on the target matrices, it has more general utilizations. Besides, it is also easy to implement. A numerical simulation illustrates fast convergence and good performance of the CVAJD.

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A fast approximate joint diagonalization algorithm using a criterion with a block diagonal weight matrix

2008 IEEE International Conference on Acoustics, Speech and Signal Processing ◽

10.1109/icassp.2008.4518361 ◽

2008 ◽

Cited By ~ 16

Author(s):

Petr Tichavsky ◽

Arie Yeredor ◽

Jan Nielsen

Keyword(s):

Weight Matrix ◽

Joint Diagonalization ◽

Diagonalization Algorithm ◽

Block Diagonal

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Nonorthogonal Joint Diagonalization Algorithm Based on Trigonometric Parameterization

IEEE Transactions on Signal Processing ◽

10.1109/tsp.2007.899378 ◽

2007 ◽

Vol 55 (11) ◽

pp. 5299-5308 ◽

Cited By ~ 15

Author(s):

Fuxiang Wang ◽

Zhongkan Liu ◽

Jun Zhang

Keyword(s):

Joint Diagonalization ◽

Diagonalization Algorithm

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Blind Separation of Cyclostationary Sources Sharing Common Cyclic Frequencies Using Joint Diagonalization Algorithm

Mathematical Problems in Engineering ◽

10.1155/2017/2546838 ◽

2017 ◽

Vol 2017 ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

Amine Brahmi ◽

Hicham Ghennioui ◽

Christophe Corbier ◽

François Guillet ◽

M’hammed Lahbabi

Keyword(s):

State Of The Art ◽

Bfgs Method ◽

Blind Separation ◽

Joint Diagonalization ◽

Mixing Matrix ◽

Update Strategy ◽

Quasi Newton ◽

Source Signals ◽

New Criteria ◽

Diagonalization Algorithm

We propose a new method for blind source separation of cyclostationary sources, whose cyclic frequencies are unknown and may share one or more common cyclic frequencies. The suggested method exploits the cyclic correlation function of observation signals to compose a set of matrices which has a particular algebraic structure. The aforesaid matrices are automatically selected by proposing two new criteria. Then, they are jointly diagonalized so as to estimate the mixing matrix and retrieve the source signals as a consequence. The nonunitary joint diagonalization (NU-JD) is ensured by Broyden-Fletcher-Goldfarb-Shanno (BFGS) method which is the most commonly used update strategy for implementing a quasi-Newton technique. The efficiency of the method is illustrated by numerical simulations in digital communications context, which show good performances comparing to other state-of-the-art methods.

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