CHENG Guanghui, WANG Leijie, WANG Zhuande. A Nonorthogonal Joint Block Diagonalization Algorithm Avoiding Degenerate Solutions[J]. Chinese Journal of Electronics, 2017, 26(2): 331-335. doi: 10.1049/cje.2016.11.009
 Citation: CHENG Guanghui, WANG Leijie, WANG Zhuande. A Nonorthogonal Joint Block Diagonalization Algorithm Avoiding Degenerate Solutions[J]. Chinese Journal of Electronics, 2017, 26(2): 331-335.

# A Nonorthogonal Joint Block Diagonalization Algorithm Avoiding Degenerate Solutions

##### doi: 10.1049/cje.2016.11.009
Funds:  This work is supported by the National Natural Science Foundation of China (No.11301056), the China Postdoctoral Science Foundation (No.2014M560709), and the Fundamental Research Funds for the Central Universities (No.20161560462).
• Rev Recd Date: 2015-08-18
• Publish Date: 2017-03-10
• The joint block diagonalization algorithm is instrumental to the convolution blind signal separation. However, the nonorthogonal joint block diagonalization algorithm based on a Weighted least-squares (WLS) criterion sometimes converges to the degenerate or trivial solution. It is simple to avoid the trivial solution by adding some constraint on the de-mixing matrix. But the degenerate solution is hard to be excluded. This paper probes the phenomenon of the degenerate solution. By adding a new penalty function to the WLS criterion, an efficient algorithm which can avoid the degenerate solution is developed. Through the theoretical derivation and numerical simulation, we can make the conclusion that the proposed algorithm is more robust and not sensitive to the square or non-square mixing matrix.
•  H. Ghennioui, E.M. Fadaili and N. Thirion-Moreau, "A nonunitary joint block diagonalization algorithm for blind separation of convolutive mixtures of sources", IEEE Signal Processing Letters, Vol.14, No.11, pp. 860-863, 2007. E.A. Moreau, "A generalization of joint-diagonalization criteria for source separation", IEEE Transaction on Signal Processing, Vol.49, No.3, pp. 530-541, 2001. Z.S. He, S. Xie and S. Ding, "Convolutive blind source separation in the frequency domain based on sparse representation", IEEE Transaction on Audio, Speech, and Language Processing, Vol.15, No.5, pp.1551-1563, 2007. H. Bousbia-Salah, A. Belouchrani and K. Abed-Meraim, "Jacobi-like algorithm for blind signal separation of convolutive mixtures", Electronics Letters, Vol.37, No.16, pp. 1049-1050, 2001. W.T. Zhang, S.T. Liu and H.M. Lu, "Fast nonunitary joint block diagonalization with degenerate solution elimination for convolutive blind source separation", Digital Signal Processing, Vol.22, No.5, pp. 808-819, 2012. H.J. Yu and D.S Huang, "Graphical representation for DNA sequences via joint diagonalization of matrix pencil", IEEE Journal of Biomedical and Health Informatics, Vol.17, No.3, pp. 503-511, 2013. D.Z. Feng, X.D. Zhang and Z. Bao, "An efficient multistage decomposition approach for independent component", Signal Processing, Vol.83, No.1, pp. 181-197, 2003. A. Yeredor, A. Ziehe and K.R. Müller, "Approximate joint diagonalization using a natural gradient approach", Independent Component Analysis and Blind Signal Separation, Vol.3195, pp. 89-96, 2004. J.F. Cardoso, "On the performance of orthogonal source separation algorithms", Proc. EUSIPCO, Vol.94, pp.776-779, 1994. C.L. Li, L.Z. Xu, S.F. Xu, et al., "A nonorthogonal approximate joint diagonalization method excluding degenerate solution for blind source separation", Journal of Computational and Theoretical Nanoscience, Vol.11, No.2, pp.353-357, 2014.

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