一种基于l1范数的欠定盲源分离算法

doi:10.3969/j.issn.1007-7162.2012.02.018

摘要/Abstract

摘要： 提出了一种基于两步法的欠定盲源分离新算法.在混叠矩阵估计阶段，采用基于势函数的聚类方法，在源信号恢复阶段，提出一种快速的稀疏信号重构算法.系统方程As (t)=x(t)的任一解, 由它的一个特解与其相对应的齐次线性方程组的一组基的线性组合之和表示，从而使原来直接估计有n个独立变量的源信号s(t)转化为估计只有n－m个独立变量的系数向量z.再借助稀疏表示实现盲源信号的分离.仿真实验验证了新算法容易实现，分离速度快，能够很好地满足盲分离对速度的要求.

关键词: 欠定盲源分离；势函数；l1范数优化模型；稀疏表示

Abstract: A new twostep algorithm for underdetermined source separation is proposed. Mixing matrix was estimated via clustering methods based on potential functions. Sources were estimated by means of a fast sparse reconstructed algorithm. Every solution to the system equation A（st)=x(t)was expressed as the sum of one of its special solution and a group of linear combination of the basic solution to the corresponding homogeneous linear equation。The number of independent variable needed for estimation was reduced from n to n m. Blind source separation of signals was done by means of sparse representation. The new algorithm is easily implemented and runs fast, which can well meet the requirements of the blind separation for speed. Simulation experiments show that the proposed algorithm has very good separation efficiency and precision.


Key words: underdetermined blind source separation; potential function; l1norm optimization model; sparse representation

谢忠德. 一种基于l1范数的欠定盲源分离算法[J]. 广东工业大学学报, 2012, 29(2): 89-93.

Xie Zhong-de. An Algorithm for Underdetermined Blind Source Separation Based on l1 norm
[J]. Journal of Guangdong University of Technology, 2012, 29(2): 89-93.

参考文献

［1］ Bell A J，Sejnowski T J.A informationmaximization approach toblind source separation and blind deconvolution［J］．NeuralComputation，1995，7(6)：1129-1159．［2］ Hyvarinen A，Oja E.A fast fixedpoint algorithm for independentcomponent analysis［J］．Neural Computation，1997，9(7)：1483-1492．

［3］谢胜利，章晋龙．基于旋转变换的最小互信息量盲分离算法［J］.电子学报，2002，30(5)：628631．

Xie Sheng-li，Zhang Jinlong．Blind separation algorithm of minimalmutual information based on rotating Transform［J］．Acta ELectronicaSinica，2002，30(5)：628-631．

［4］ Hyvarinen A．Blind source separation by nonstationarity of vailanee：a cumulantbased approach［J］．IEEE Trans Neural Network， 2001，12(6)：1126-1143．

［5］ Comon P．Independent component analysisa new concept?［J］．SignalProcessing，1994，36(2)： 287-314．

［6］ Matsuoka K，Ohya M，Kawamoto M．A neural net for blind separationof nonstationary signal［J］．Neural Networks，1995，8(3)：41 l-419．

［7］ Belouchrani A，Cardoso J F．Maximum likelihood source separationfor discrete sourees［C］∥Proc．EUSIPCO,Edinburgh,Scotland：［s.n.］，1994：768-771．

［8］ Zibulevsky M，Pearlmutter B A．Blind source separation by sparsedecomposition in a signal dictionary［J］．Neural Computation，2001，13 (4)：863-882．

［9］ Lee T W，Lewieki M S，Girolami M，et a1．Blind source separationof nlore sources than mixtures using overcomplete representation［J］． IEEE Signal Processing Letter，1999，6(4)：8790．

［10］ Lewicki M S，Sejnowski T J．Learning overcomplete representations［J］． Neural Computation，2000，12(2)：337-365．

［11］ Li Yuanqing，Ciehocki，Andrzej，et a1．Analysis of sparse representation and blind source separation［J］．Neural Computation，2004，16 (6)：1193-1234．

［12］ Bofill P，Zibulevsky M．Underdetermined source separation usingsparse representation［J］．Signal Processing，2001，81(11)：2353-2362．

［13］ Bofill P，Zibulevsky M．Blind separation of more sources than mixtures using sparsity of their shorttime fourier transform［C］∥Proc.Independent Component Analysis，Helsinki,Finland：［s.n.］，2000：87-92．

［14］ Theis F，Lang E，Formalization of the twostep approach toovercomplete BSS［C］∥Proc.SIP, Regensburg,Germany：［s.n.］，2002：207212．

［15］ Takigawa I，Toyama J．Performanee analysis of minimum L1norln solutions for underdetermined source separation［J］．IEEE TransSignal Processing，2004，52(3)：582-591．

［16］ Zibulevsky M,Kisilev P,Zeevi Y Y,et al. Blind source separation via multinode sparserepresentation ［C］∥Advances in Neural Information Processing Systems.Cambridge,MA,USA:MIT,2002：1049-1056.

［17］ Lin J K,Grier D G,Cowan J D. Feature extraction approach to blind source separation［C］∥Proceedings of theIEEE Workshop on Neural Networks for Signal Processing.Amelia Island, FL,USA:IEEE,1997：398-405.

［18］ Donoho D.Compressive sampling［J］.IEEE Trans on Information Theory,2006,52(4):1289-1306.

［19］ Kim SJ, Koh K, Lustig M,et al.An InteriorPoint Method for LargeScale 11Regularized Least Squares［J］.IEEE Journal on Selected Topics in Signal Processing, Dec 2007,1(4):606-617.

［20］ Irina F Gorodnitskya, John S Georgeb，Bhaskar D Raoa.Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm［J］. Electroencephalography and Clinical Neurophysiology, 1995, 95（4）： 231-251. 

［21］〖WB〗傅予力，谢胜利，何昭水．稀疏盲源信号分离的新算法［J］.计算机工程与应用，2007，43(9)：84-87．

〖DW〗Fu Yuli,Xie Shengli,He Zhaoshui.A new algorithm for blind source separation of spare signal［J］.Computer Engineering and Applications,2007,43(9):84-87.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed