Generalized Unitary Joint Diagonalization algorithm based on approximate Givens rotations

Like the Joint Diagonalization of a unique set of matrices, Generalized Joint Diagonalization is an algebraic problem encountered in different applications such as data fusion and blind source separation. This paper proposes a new generalized unitary joint diagonalization approach based on the Jacob...

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Bibliographic Details
Published in:IEEE signal processing letters Vol. 31; pp. 1 - 5
Main Authors: Azzouz, Malika, Mesloub, Ammar, Abed-Meraim, Karim, Belouchrani, Adel
Format: Journal Article
Language:English
Published: New York IEEE 01.01.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects:
Algorithms
Approximation
Approximation algorithms
Convergence
Covariance matrices
Criteria
Data integration
Engineering Sciences
Estimation
Generalized Unitary Joint Diagonalization (GUJD)
Givens rotations
Iterative methods
Jacobi iterative algorithm
Jacobian matrices
Joint Blind Source Separation (JBSS)
Mathematical models
Parameters
Signal and Image processing
Signal processing algorithms
ISSN:1070-9908, 1558-2361
Online Access:Get full text
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Summary:Like the Joint Diagonalization of a unique set of matrices, Generalized Joint Diagonalization is an algebraic problem encountered in different applications such as data fusion and blind source separation. This paper proposes a new generalized unitary joint diagonalization approach based on the Jacobi iterative scheme using Givens rotations and simplified criterion, introducing three approximations. These approximations allowed us to reach a simultaneous estimation of different parameters. The first appears in the simplified criterion composed of entries doubly affected by the Givens rotations. The second approximation is in the Givens parameter using a small amplitude angle. The last approximation resides in keeping only the first order of transformed entries. Numerical experiments, including examples of joint blind audio source separation, are provided. The results show the effectiveness of the developed algorithm as compared to existing ones. The simultaneous estimation of different Givens rotations improves the algorithm's computation complexity and convergence rate
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ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2023.3342705