A fast algorithm for nonunitary joint diagonalization and its application to blind source separation

Xian-Feng Xu; Da-Zheng Feng; Wei Xing Zheng

doi:10.1109/TSP.2011.2141667

A fast algorithm for nonunitary joint diagonalization and its application to blind source separation

Xian-Feng Xu, Da-Zheng Feng, Wei Xing Zheng

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

Abstract

A fast algorithm, named Complex-Valued Fast Frobenius DIAGonalization (CVFFDIAG), is proposed for seeking the nonunitary approximate joint diagonalizer of a given set of complex-valued target matrices. It adopts a multiplicative update to minimize the Frobenius-norm formulation of the approximate joint diagonalization problem. At each of multiplicative iterations, a strictly diagonally dominant updated matrix is obtained. This scheme ensures the invertibility of the diagonalizer. The CVFFDIAG relaxes several constraints on the target matrices and thus has much general applications. Furthermore, the special approximation of the cost function, the ingenious utilization of some structures and the adequate notation of concerned variables lead to the high computational efficiency of the proposed algorithm. Numerical simulations are conducted to illustrate good performances of the CVFFDIAG.

Original language	English
Pages (from-to)	3457-3463
Number of pages	7
Journal	IEEE Transactions on Signal Processing
Volume	59
Issue number	7
DOIs	https://doi.org/10.1109/TSP.2011.2141667
Publication status	Published - 2011

Keywords

algorithms
blind source separation
Frobenius algebras
approximation algorithms
signal processing

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10.1109/TSP.2011.2141667

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title = "A fast algorithm for nonunitary joint diagonalization and its application to blind source separation",

abstract = "A fast algorithm, named Complex-Valued Fast Frobenius DIAGonalization (CVFFDIAG), is proposed for seeking the nonunitary approximate joint diagonalizer of a given set of complex-valued target matrices. It adopts a multiplicative update to minimize the Frobenius-norm formulation of the approximate joint diagonalization problem. At each of multiplicative iterations, a strictly diagonally dominant updated matrix is obtained. This scheme ensures the invertibility of the diagonalizer. The CVFFDIAG relaxes several constraints on the target matrices and thus has much general applications. Furthermore, the special approximation of the cost function, the ingenious utilization of some structures and the adequate notation of concerned variables lead to the high computational efficiency of the proposed algorithm. Numerical simulations are conducted to illustrate good performances of the CVFFDIAG.",

keywords = "algorithms, blind source separation, Frobenius algebras, approximation algorithms, signal processing",

author = "Xian-Feng Xu and Da-Zheng Feng and Zheng, {Wei Xing}",

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T1 - A fast algorithm for nonunitary joint diagonalization and its application to blind source separation

AU - Xu, Xian-Feng

AU - Feng, Da-Zheng

AU - Zheng, Wei Xing

PY - 2011

Y1 - 2011

N2 - A fast algorithm, named Complex-Valued Fast Frobenius DIAGonalization (CVFFDIAG), is proposed for seeking the nonunitary approximate joint diagonalizer of a given set of complex-valued target matrices. It adopts a multiplicative update to minimize the Frobenius-norm formulation of the approximate joint diagonalization problem. At each of multiplicative iterations, a strictly diagonally dominant updated matrix is obtained. This scheme ensures the invertibility of the diagonalizer. The CVFFDIAG relaxes several constraints on the target matrices and thus has much general applications. Furthermore, the special approximation of the cost function, the ingenious utilization of some structures and the adequate notation of concerned variables lead to the high computational efficiency of the proposed algorithm. Numerical simulations are conducted to illustrate good performances of the CVFFDIAG.

AB - A fast algorithm, named Complex-Valued Fast Frobenius DIAGonalization (CVFFDIAG), is proposed for seeking the nonunitary approximate joint diagonalizer of a given set of complex-valued target matrices. It adopts a multiplicative update to minimize the Frobenius-norm formulation of the approximate joint diagonalization problem. At each of multiplicative iterations, a strictly diagonally dominant updated matrix is obtained. This scheme ensures the invertibility of the diagonalizer. The CVFFDIAG relaxes several constraints on the target matrices and thus has much general applications. Furthermore, the special approximation of the cost function, the ingenious utilization of some structures and the adequate notation of concerned variables lead to the high computational efficiency of the proposed algorithm. Numerical simulations are conducted to illustrate good performances of the CVFFDIAG.

KW - algorithms

KW - blind source separation

KW - Frobenius algebras

KW - approximation algorithms

KW - signal processing

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DO - 10.1109/TSP.2011.2141667

M3 - Article

SN - 1053-587X

VL - 59

SP - 3457

EP - 3463

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 7

ER -

A fast algorithm for nonunitary joint diagonalization and its application to blind source separation

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