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基于奇異值分解的超定盲信號分離

朱孝龍,  張賢達

朱孝龍, 張賢達. 基于奇異值分解的超定盲信號分離[J]. 電子與信息學報, 2004, 26(3): 337-343.
引用本文: 朱孝龍, 張賢達. 基于奇異值分解的超定盲信號分離[J]. 電子與信息學報, 2004, 26(3): 337-343.
Zhu Xiao-long, Zhang Xian-da. Overdetermined Blind Source Separation Based on Singular Value Decomposition[J]. Journal of Electronics & Information Technology, 2004, 26(3): 337-343.
Citation: Zhu Xiao-long, Zhang Xian-da. Overdetermined Blind Source Separation Based on Singular Value Decomposition[J]. Journal of Electronics & Information Technology, 2004, 26(3): 337-343.

基于奇異值分解的超定盲信號分離

Overdetermined Blind Source Separation Based on Singular Value Decomposition

  • 摘要: 該文研究超定盲信號分離,即觀測信號個數(shù)不少于源信號個數(shù)情況下的盲信號分離問題。作者 從分離矩陣的奇異值分解出發(fā),首先提出一種基于獨立分量分析的超定盲信號分離代價函數(shù),接著推導了一般梯度學習算法。此后,借助于相對梯度的概念,證明超定盲信號分離與通常的完備盲信號分離具有相同形式的自然梯度算法。仿真試驗驗證了算法的有效性。
    Abstract: The problem of overdetermined Blind Source Separation (BSS) where there are more mixtures than sources is considered. Beginning with the Singular Value Decompo sition (SVD) of the separation matrix, a cost function is presented based on Independent Component Analysis (ICA), and then the ordinary gradient learning algorithm is developed. Secondly, resorting to the relative gradient, it is shown that the natural gradient learning algorithm for overdetermined BSS has the same form as that for usual complete BSS, which is verified by simulation results.
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  • Bell A J, Sejnowski T J. An information-maximization approach to blind separation and blind deconvolution[J].Neural Computation.1995, 7(6):1129-1159[2]Karhunen J, Joutsensalo J. Representation and separation of signals using nonlinear pca type learning[J].Neural Networks.1994, 7(1):113-127[3]Karhunen J, Pajunen J, Oja E. The nonlinear PCA criterion in blind source separation: Relations with other approaches[J].Neurocomputing.1998, 22(1):5-20[4]Comon P. Independent component analysis, a new concept? Signal Processing, 1994, 36(3): 287-314.[5]Amari S I.[J].Cichocki A, Yang H H. A new learning algorithm for blind signal separation. In D.S. Touretzky, M. C. Mozer M. E. Hasselmo (Eds.), Advance in Neural Information Processing Systems, Cambridge, MA: MIT Press.1996,:-[6]Cardoso J F, Laheld B. Equivariant adaptive source separation[J].IEEE Trans. on Signal Process ing.1996, 44(12):3017-3030[7]Yang H H, Amari S I. Adaptive on-line learning algorithms for blind separation-maximum entropy and minimum mutual information[J].Neural Computation.1997, 9(5):1457-1482[8]Amari S I. Natural gradient learning for over- and under-complete bases in ICA[J].Neural Computation.1999, 11(8):1875-1883[9]Zhang L Q, Cichocki A, Amari S I. Natural gradient algorithm for blind separation of overdetermined mixture with additive noise[J].IEEE Signal Processing Letters.1999, 6(11):293-295[10]Choi S, Cichocki A, Zhang L Q, Amari S I. Approximate maximum likelihood source separation using natural gradient. 3rd IEEE Signal Processing Workshop on Signal Processing Advances in Wireless Communications, Taoyuan, Taiwan, 2001: 20-23.[11]Lee T W, Lewicki M S, Girolami M, Sejnowski T J. Blind source separation of more sources than mixtures using overcomplete representations[J].IEEE Signal Processing Letters.1999, 6(4):87-90[12]Lewicki M S, Sejnowski T J. Learning overcomplete representation[J].Neural Computation.2000,12(2):337-365[13]張賢達.信號處理中的線性代數(shù).北京:科學出版社,1997,第6章.[14]Amari S I. Natural gradient works efficiently in learning[J].Neural Computation.1998, 10(2):251-276
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出版歷程
  • 收稿日期:  2002-08-30
  • 修回日期:  2003-03-28
  • 刊出日期:  2004-03-19

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