Advanced Search
Volume 32 Issue 5
May  2010
Turn off MathJax
Article Contents
Zhang Yan-liang, Lou Shun-tian, Zhang Wei-tao. A Study of Identifiability for Blind Signal Separation via Nonorthogonal Joint Diagonalization[J]. Journal of Electronics & Information Technology, 2010, 32(5): 1066-1070. doi: 10.3724/SP.J.1146.2009.00750
Citation: Zhang Yan-liang, Lou Shun-tian, Zhang Wei-tao. A Study of Identifiability for Blind Signal Separation via Nonorthogonal Joint Diagonalization[J]. Journal of Electronics & Information Technology, 2010, 32(5): 1066-1070. doi: 10.3724/SP.J.1146.2009.00750

A Study of Identifiability for Blind Signal Separation via Nonorthogonal Joint Diagonalization

doi: 10.3724/SP.J.1146.2009.00750
  • Received Date: 2009-05-15
  • Rev Recd Date: 2009-12-01
  • Publish Date: 2010-05-19
  • Based on the uniqueness condition of the solution of Nonorthogonal Joint Diagonalization (NJD), the identifiability for Blind Signal Separation (BSS) is analyzed. Firstly, it is proved that the target matrices consisting of Second-Order Statistics (SOS) or higher-order cumulant are diagonalizable, so the problem of BSS can be solved by NJD. The uniqueness condition for NJD is that the vectors consisting of diagonal elements in the same position of diagonal matrix are pairwise linearly independent. From this proposition,the necessary and sufficient condition for BSS is deduced. For second-order statistics based BSS, the condition is that the source signals have not the identical autocorrelation shape. For higher-order cumulant, there is not Gaussian signal in sources. The above conclusion provides a mathematical foundation for the BSS methods based on the NJD. Numerical simulations confirm the conclusion in this paper.
  • loading
  • Cardoso J F and Souloumiac A. Blind beamforming for non Gaussian signals[J].IEE Proceedings, Part F: Radar and Signal Processing.1993, 140(6):362-370[2]Belouchrani A, Meraim K, Cardoso J F, and Moulines E. A blind source separation technique using second-order statistics[J].IEEE Transactions on Signal Processing.1997, 45(2):434-444[3]Yeredor A. Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation[J].IEEE Transactions on Signal Processing.2002, 50(7):1545-1553[4]Ziehe A, Laskov P, Nolte G, and Mller K R.A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation[J]. Journal of Machine Learning Research, 2004, 5(12): 777-800.[5]Li X L and Zhang X D. Nonorthogonal joint diagonalization free of degenerate solution[J].IEEE Transactions on Signal Processing.2007, 55(5):1803-1814[6]Wang Fu-xiang, Liu Zhong-kan, and Zhang Jun. Nonorthogonal joint diagonalization algorithm based on trigonometric parameterization[J].IEEE Transactions on Signal Processing.2007, 55(11):5299-5308[7]Souloumiac A. Non-orthogonal joint diagonalization by combining givens and hyperbolic rotations[J].IEEE Transactions on Signal Processing.2009, 57(6):2222-2231[8]Zhang Hua, Feng Da-zheng, and Zheng Wei-xing. A study of identifiability for blind source separation via nonorthogonal joint diagonalization[C]. IEEE International Symposium on Circuits and Systems, Seattle, Washington, USA, 2008: 3230-3233.[9]Comon P. Canonical tensor decompositions[R]. Technology report, Laboratory of Information Signal System, French National Center for Scientific Research, June, 2004.[10]Giorgio T and Rasmus B. A comparison of algorithms for tting the PARAFAC model[J].Computational Statistics and Data Analysis.2006, 50(7):1700-1734[11]De Lathauwer L. A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization[J]. SIAM Journal on Matrix Analysis and Applications, 2006, (28): 642-666.[12]李细林. 盲信号分离中的联合对角化和相位恢复问题研究[D]. [博士论文],清华大学,2008.[13]Li Xi-lin. Studies on joint diagonalization and phase recovery in blind soure separation[D]. [Ph.D. dissertation], Tsinghua University, 2008.[14]Ten Berge J M F and Sidiropoulos N D. On uniqueness in CANDECOMP/PARAFAC[J]. Psychometrika, 2002, (67): 399-409.[15]Cao Xi-ren and Liu Ruey-wen. General approach to blind source separation[J].IEEE Transactions on Signal Processing.1996, 44(3):562-571
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (4172) PDF downloads(996) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return