盲信号分离的原理及其关键问题的研究
|
摘要
盲源分离是上世纪80年代初在信号处理领域诞生的备受学术界关注的新生学科,在许多新兴领域都有着重要的应用。盲分离按照其混叠方式的不同,可分为瞬时线性混叠和非线性混叠。本文着重研究主要针对盲分离瞬时线性混叠模型的适定、欠定情形以及卷积混叠模型,具体的工作包括如下几个方面:
1.针对适定线性混叠的情形,深入研究了如何把联合对角化技术应用于解决盲信号分离问题。利用信号时序结构的二阶统计量方法通常需要解决一个联合对角化问题。首先对一类特殊的矩阵束——良态矩阵束给出了一个新算法。由于采用了共轭梯度算法优化目标函数,算法不仅收敛快,而且收敛性有保证。然后,给出了可完美对角化的判别定理。同时,还把对角化问题转化为含有R-正交约束的一类优化问题,给出了统一的优化框架。
2.在线性欠定混叠盲分离以及稀疏分量分析中,如果信号是非严格稀疏时,通常的两步法将失去作用,前人提出了源信号非严格稀疏下的k-SCA条件,并给出了在此条件下,混叠矩阵能被估计以及源信号可恢复的理论证明,但目前甚少相关的具体实现算法。文中首先提出了一种针对k-SCA条件,利用超平面聚类转化为其法线聚类来估计混叠矩阵的有效算法,在源信号重建上,还提出了一种简化l1范数解的新算法,弥补了该领域研究的一个缺失。
3.同样是针对线性欠定混叠的情形,提出利用基于单源区间的盲分离算法。采用Bofill的两步法,第一步估计混叠矩阵,第二步恢复源信号。首次发现了暂时非混叠性这一混叠信号的物理性质,并定义了单源区间,提出了一个基于最小相关系数的统计稀疏分解准则(SSDP)。并在此基础上,提出了非完全稀疏性的问题。现有的最短路径法、l1范数解和SSDP算法仅适用于稀疏源而不适宜非完全稀疏源。针对两个观测信号的情形,提出了统计非稀疏准则(SNSDP)。该准则将信号分成若干区间,用源的相关性判断各区间是否非完全稀疏,并在非完全稀疏和稀疏的区间采取不同的源恢复策略。它改善了估计的源信号。最后,语音信号的仿真实验显示它的性能和实用性。
4.针对卷积混叠模型。提出了一种自适应盲解卷算法,该算法不要求源信号独立同分布、也不要求源信号平稳。特别是,对于混叠信号数目少于源信号数目情况下,算法能够实现卷积盲分离,扩大了卷积盲分离的应用范围。
仿真与分析表明,本文所提出的算法能有效地解决线性混叠和卷积混叠的部分问题,巩固了盲分离理论和方法的基础,展现了盲分离研究领域的发展前景。
Blind Source Separation (BSS) is a new research branch in signal processing that original developed in the 1980s. After that, BSS has gained much more attention. BSP has its potential applications in many key fields. According to the mixing form, BSS can be categorized into two main directions, such as instant linear mixing case and nonlinear mixing case. This dissertation focuses on well-determined case and under-determined case of linear mixture and convolutive mixture for blind source separation theorems, algorithms, and applications, including:
1. For well-determined linear mixture, the joint diagonalization technique is used for solve BSS problem. Usually, the second order statistics method based on sequential structure must solve a joint diagonalization problem. Firstly, a new algorithm is given for a kind of sepecial matrix pencil (Well-Matrix Pencil). With objective function optimized by conjugated gradient algorithm, the new algorithm can convegent quickly. Then, the perfect diagonalization theorem is given. The joint diagonalization problem had been turned into a R-Orthogonal constraint problem. And a universal optimization framework is also put forward.
2. In the under-determined linear mixing case and sparse component analysis, if the signal is not strictly sparse, the traditional“two steps”method cannot function. Some previous works proposed K-SCA condition, the prove of the estimation for mixing matrix and recoverable for source in non-strictly sparse case. But few works concern about the algorithm in detail. A new efficient algorithm is proposed in this paper based on mixing matrix estimated by normal clustering instead of hyperplane clustering. For the sources recovery, a algorithm of compact l1-norm solution is also proposed to make up the absence in this area.
3. Also for underterminded linear mixture, a new bss algorithm based on single source interval is proposed. With Bofill two-step method, estimate the mixture matrix in the first step and then recover the source signal. For the first time, we discover the temporary unmixing physical property and define the single source interval. A sparse decomposition principle based on minimized correlative coefficient has been proposed and it is called statistical sparse decomposition principle (SSDP). Based on it, the incompletely sparsity problem is also put forward. The shorest path algorithm, l1-norm solution and SSDP algorithm is fit for sparse source but not incompletely sparse source. Statistically non-sparse decomposition principle (SNSDP) is proposed for two observed signals. The principle firstly divides the signals into many intervals, and then decides whether they are incompletely sparse using correlative of sources, and then utilizes different recovery strategy in the sparse and incompletely sparse intervals. It overcomes the shortcoming of these current algorithms and improves the estimated sources. Finally, mixed speech signals are used to show its performance for blind source separation in the simulations.
4. For underdetermined convolutive mixture, a convolutive BSS algorithm in the frequency domain has been proposed. The algorithm does not imposes the condition that source signals are identically distributed(iid) and stable. Especially, the mixture signals’number is smaller than sources’, the observed signals can also theoretically be separated. And it extends the application field of BSS in some degree.
Simulations and analysis show that the proposed algorithms can partly solve the problems of linear or convolutive mixture. They make the basis of BSS theory and methods stronger and reveal the foreground of BSS’s field.
1.针对适定线性混叠的情形,深入研究了如何把联合对角化技术应用于解决盲信号分离问题。利用信号时序结构的二阶统计量方法通常需要解决一个联合对角化问题。首先对一类特殊的矩阵束——良态矩阵束给出了一个新算法。由于采用了共轭梯度算法优化目标函数,算法不仅收敛快,而且收敛性有保证。然后,给出了可完美对角化的判别定理。同时,还把对角化问题转化为含有R-正交约束的一类优化问题,给出了统一的优化框架。
2.在线性欠定混叠盲分离以及稀疏分量分析中,如果信号是非严格稀疏时,通常的两步法将失去作用,前人提出了源信号非严格稀疏下的k-SCA条件,并给出了在此条件下,混叠矩阵能被估计以及源信号可恢复的理论证明,但目前甚少相关的具体实现算法。文中首先提出了一种针对k-SCA条件,利用超平面聚类转化为其法线聚类来估计混叠矩阵的有效算法,在源信号重建上,还提出了一种简化l1范数解的新算法,弥补了该领域研究的一个缺失。
3.同样是针对线性欠定混叠的情形,提出利用基于单源区间的盲分离算法。采用Bofill的两步法,第一步估计混叠矩阵,第二步恢复源信号。首次发现了暂时非混叠性这一混叠信号的物理性质,并定义了单源区间,提出了一个基于最小相关系数的统计稀疏分解准则(SSDP)。并在此基础上,提出了非完全稀疏性的问题。现有的最短路径法、l1范数解和SSDP算法仅适用于稀疏源而不适宜非完全稀疏源。针对两个观测信号的情形,提出了统计非稀疏准则(SNSDP)。该准则将信号分成若干区间,用源的相关性判断各区间是否非完全稀疏,并在非完全稀疏和稀疏的区间采取不同的源恢复策略。它改善了估计的源信号。最后,语音信号的仿真实验显示它的性能和实用性。
4.针对卷积混叠模型。提出了一种自适应盲解卷算法,该算法不要求源信号独立同分布、也不要求源信号平稳。特别是,对于混叠信号数目少于源信号数目情况下,算法能够实现卷积盲分离,扩大了卷积盲分离的应用范围。
仿真与分析表明,本文所提出的算法能有效地解决线性混叠和卷积混叠的部分问题,巩固了盲分离理论和方法的基础,展现了盲分离研究领域的发展前景。
Blind Source Separation (BSS) is a new research branch in signal processing that original developed in the 1980s. After that, BSS has gained much more attention. BSP has its potential applications in many key fields. According to the mixing form, BSS can be categorized into two main directions, such as instant linear mixing case and nonlinear mixing case. This dissertation focuses on well-determined case and under-determined case of linear mixture and convolutive mixture for blind source separation theorems, algorithms, and applications, including:
1. For well-determined linear mixture, the joint diagonalization technique is used for solve BSS problem. Usually, the second order statistics method based on sequential structure must solve a joint diagonalization problem. Firstly, a new algorithm is given for a kind of sepecial matrix pencil (Well-Matrix Pencil). With objective function optimized by conjugated gradient algorithm, the new algorithm can convegent quickly. Then, the perfect diagonalization theorem is given. The joint diagonalization problem had been turned into a R-Orthogonal constraint problem. And a universal optimization framework is also put forward.
2. In the under-determined linear mixing case and sparse component analysis, if the signal is not strictly sparse, the traditional“two steps”method cannot function. Some previous works proposed K-SCA condition, the prove of the estimation for mixing matrix and recoverable for source in non-strictly sparse case. But few works concern about the algorithm in detail. A new efficient algorithm is proposed in this paper based on mixing matrix estimated by normal clustering instead of hyperplane clustering. For the sources recovery, a algorithm of compact l1-norm solution is also proposed to make up the absence in this area.
3. Also for underterminded linear mixture, a new bss algorithm based on single source interval is proposed. With Bofill two-step method, estimate the mixture matrix in the first step and then recover the source signal. For the first time, we discover the temporary unmixing physical property and define the single source interval. A sparse decomposition principle based on minimized correlative coefficient has been proposed and it is called statistical sparse decomposition principle (SSDP). Based on it, the incompletely sparsity problem is also put forward. The shorest path algorithm, l1-norm solution and SSDP algorithm is fit for sparse source but not incompletely sparse source. Statistically non-sparse decomposition principle (SNSDP) is proposed for two observed signals. The principle firstly divides the signals into many intervals, and then decides whether they are incompletely sparse using correlative of sources, and then utilizes different recovery strategy in the sparse and incompletely sparse intervals. It overcomes the shortcoming of these current algorithms and improves the estimated sources. Finally, mixed speech signals are used to show its performance for blind source separation in the simulations.
4. For underdetermined convolutive mixture, a convolutive BSS algorithm in the frequency domain has been proposed. The algorithm does not imposes the condition that source signals are identically distributed(iid) and stable. Especially, the mixture signals’number is smaller than sources’, the observed signals can also theoretically be separated. And it extends the application field of BSS in some degree.
Simulations and analysis show that the proposed algorithms can partly solve the problems of linear or convolutive mixture. They make the basis of BSS theory and methods stronger and reveal the foreground of BSS’s field.
引文
[1] C. Jutten, J. Herault. Blind separation of sources, Part I: An adaptive algorithm based on neuromimetic[J]. Signal Processing, 1991, 24(1):1-10.
[2] A. Hyvarinen, E. Oja, Independent component analysis: algorithms and applications[J]. Neural Networks, June 2000, 13(4-5):411-430.
[3] A. Cichocki, S. Amari, Adaptive blind signal and image processing: learning algorithms and applications[M] John Wiley and Sons, LTD, June 2002.
[4] H. Sahlin, H. Broman, Separation of real-world signals[J]. Signal Processing, 1998, 64(2): 103-113.
[5] J. Joutsensalo and P.Pajunen. Blind Symbol Learning Algorithms for CDMA System[C]. Int Joint Conf. On Neural Networks, (IJCNN’98), Anchorage, Alaska, May 4-9,1998, 1:152-155.
[6] J. Joutsensalo and Ristaniemi, Blind Multi-User Detection by Fast Fixed Point Algorithm without Prior Knowledge of Symbol-Level Timing[C]. Proc. IEEE Signal Processing Workshop on Higher Order Statistics, Ceasarea, Israel, June 14-16, 1999, 305-308.
[7] T. Ristaniemi and J. Joutsensalo, Independent component analysis with code information utilization in DS-CDMA signal separation[C]. Proc. IEEE GLOBECOM’99, Riode Janeiro, Brazil, December 5-9, 1999, 1a: 320-324.
[8] R. Cristescu, J. Joutsensalo and T. Ristaniemi, Fading ChannelEstimation by Mutual Information Minimization for Gaussian Stochastic Processes[C]. Proc. IEEE International Conference on Communications, New Orleans, LA, 18-22 June, 2000:56-59.
[9] S. Talwar, M. Viberg, and A. Paulraj. Blind estimation of multiple co-channel digital signals using an antenna array[J]. IEEE Signal Processing Letters, February 1994, 1(2):29–31.
[10] S. Talwar, M. Viberg, and A. Paulraj. Blind estimation of synchronous co-channel digital signals using an antenna array. Part I: Algorithms[J]. IEEE Trans. Signal Processing, May 1996, 44(5): 1184–1197.
[11]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.
[12]倪晋平,马远良等,用独立分量分析算法实现水声信号盲分离[J],声学学报,2002,27(4):321-326.
[13]张安清,章新华,基于信息理论的舰船噪声盲分离算法[J],系统工程与电子技术,2002,24(1):38-41.
[14] Y. Feng, V. Zarzoso, A.K. Nandi, WDM monitoring through blind signal separation[C]. Optical Fiber Communication Conference and Exhibit, 2002. OFC 2002, 17-22 March 2002, 746-748.
[15] Y.M. Feng; V. Zarzoso, A.K. Nandi, WDM monitoring using blind signal separation based on higher-order statistics[C]. 14th International Conference on Digital Signal Processing, July 2002, 1:1-3.
[16]斯华龄,张立明,智能视觉图像处理,上海:上海科技教育出版社,2002年10月第1版。
[17] S. Choi, A. Cichocki, H. M. Park, et al. Blind source separation and independent component analysis: A review. Neural Information Processing - Letters and Reviews[J]. January 2005, 6(1):1-57
[18] L. Molgedey, H.G. Schuster. Separation of a mixture of independent signals using time delayed correlations[J].Physical Review Letters, 1994,72(23):3634-3637.
[19] A. Beloouchrani, A.M. Karim, J.F. Cardoso, et al. A blind source separation technique using second-order statistics[J]. IEEE Trans. Signal Process, 1997,45 (2):434-443.
[20] A. Ziehe, K. R.M¨uller, G. Nolte, et al. Artifact reduction in biomagnetic recordings based on time-delayed second order correlations[J]. IEEE Trans. on Biomedical Engineering, 2000, 47: 75-87.
[21] S. Choi, A. Cichocki, L. Zhang, et al. Approximate maximum likelihood source separation using the natural gradient[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, January 2003, E86-A(1):198-205.
[22] A. Cichocki, A. Belouchrani. Sources separation of temporally correlated sources from noisy data using bank of band-pass filters[C]. In Third International Conference on Independent Component Analysis and Signal Separation (ICA-2001), San Diego, USA, Dec. 2001, 173-178.
[23] K. Matsuoka, M. Ohya, M. Kawamoto. A neural net for blind separationof nonstationary signals[J].Neural Networks, 1995, 8(3):411-419.
[24] S. Choi, A. Cichocki, A. Belouchrani. Second order nonstationary source separation[J]. Journal of VLSI Signal Processing,August 2002, 32(1–2):93-104.
[25] L. Parra, C. Spence. Convolutive blind source separation of non-stationary sources[J]. IEEE Trans. Speech and Audio Processing, May 2000,8(3):320-327.
[26] A. Belouchrani, M.G. Amin. A new approach for blind source separation using time-frequency distributions[J].Proc. SPIE, 1996, 2846:193-203.
[27] O. Yilmaz, S. Rickard. Blind separation of speech mixtures via time-frequency masking[J]. IEEE trans on signal processing. 52(7): 1830-1847.
[28] F. Abrard, Y. A. Deville. Time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources[J]. Signal processing 2005,85:1389-1403
[29] S. Rickard, T. Melia, C. Fearon. DESPRIT - histogram based blind source separation of more sources than sensors using subspace methods[C]. Proceedings of the IEEE Workshop on Applications of Signal Processing in Audio and Acoustics, New Paltz, NY, USA, October 2005, 5-8.
[30] T. Melia, S. Rickard, C. Fearon. Extending the DUET blind source separation technique[C]. Proceedings of Signal Processing with Adaptative Sparse Structured Representations Workshop (SPARS '05), Rennes, France, November 2005.
[31] K. R. M¨uller, P. Philips, A. Ziehe. JADETD: Combining higher-order statistics and temporal information for blind source separation (with noise)[C]. Proc. ICA’99, Aussois, France, 1999,87-92.
[32] A. Belouchrani. Separation Autodidacte de Sources: Algorithme, Performances et Application a des Signaux Exp′erimentaux[D]. PhD thesis, ENST, Telecom Paris, July 1995.
[33] A. Cichocki, S. Amari. Adaptive blind signal and image processing: learning algorithms and applications[M].John Wiley and Sons, LTD, June 2002.
[34] L. Tong, R. Liu, V.C. Soon, et al, Indeterminacy and identifiability of blind identification[J]. IEEE Trans on Circuits and systems, 1991, vol. 38(5):499-506.
[35] A. Belouchrani, K. Abed-Meraim, J. F. Cardoso, et al. A blind source separation techniqueusing second-order statistics[J]. IEEE Trans. Signal Processing, February 1997, 45(2): 434–444.
[36] G. H. Golub, C. F. Van Loan. Matrix Computations[J]. 2nd edition. Johns Hopkins, 1993.
[37] J. F. Cardoso. Jacobi angles for simultaneous diagonalization[J]. SIAM J. Mat. Anal. Appl, 1996, 17(1): 161–164.
[38] D. T. Pham. Joint approximate diagonalization of positive definite hermitian matrices[C]. Technical Report LMC/IMAG, University of Grenoble, France, 2000.
[39] Y.Q. Li, J. Wang, J.M. Zurada, Blind extraction of singularly mixedsource signals[J]. IEEE Trans on Neural Networks, 2000, 11(6):1413-1422.
[40] Y.Q. Li, J. Wang, Sequential blind extraction of instantaneously mixed sources[J]. IEEE Trans. Signal processing, May 2002, 50(5): 997-1006.
[41] A. Belouchrani, J.F. Cardoso, Maximum likelihood source separation for discrete sources[C]. in Proc. EUSIPCO, 1994, 768-771.
[42] M. Zibulevsky, B.A. Pearlmutter, Blind source separation by sparse decomposition in a signal dictionary[J]. Neural computation, April 2001, 13(4): 863-882.
[43] T. W. Lee, M.S. Lewicki, M. Girolami, T.J. Sejnowski, Blind source separation of more sources than mixtures using overcomplete representation[J]. IEEE Signal processing letter, 1999, 6(4): 87-90.
[44] M.S. Lewicki, T.J. Sejnowski, Learning overcomplete representations[J]. Neural computation, 2000, 12:337-365.
[45] Y.Q. Li, A. Cichocki, S. Amari, Analysis of sparse representation and blind source separation[J]. Neural computation, June 2004, 16(6): 1193-1234.
[46] P. Bofill, M. Zibulevsky, Underdetermined source separation using sparse representation[J]. Signal processing, 2001, 81: 2353-2362.
[47] B.A. Pearlmutter, V.K. Potluru, Sparse separation: Principles and tricks[C]. Proc SPIE "Independent Component Analyses, Wavelets, and Neural Networks", April 2003, 5102:1-4.
[48] I.F. Gorodnitsky and B.D. Rao. Sparse signal reconstruction fromlimited data using FOCUSS: A recursive weighted minimum norm algorithm[J]. IEEE Trans. SP, 1997, 45(3): 600-616.
[49] S.F. Cotter, B.D. Rao, K. Engan et al. Sparse solutions to linear inverse problems with multiple measurement vectors[J]. IEEE Trans. Signal Processing, 2005, 53(7): 2477–2488.
[50] A. Taleb, C. S. Jutten, A. Xichocki. Information back-propagation for blind separation of sources from non-linear mixtures: An entropy-based algorithm[C]. in Proc of ICASSP. Washinton, ICASSP, 1998, 2089-2092.
[51] A. Taleb, C. Jutten. Source separation in post-nonlinear mixtures[J]. IEEE Trans. Signal Processing, October 1999, 47 (10):2807-2820.
[52] P. Pahybeb, A. Hyvarinen, J. Karhunen. Nonlinear blind source separation by self-organizating maps[C]. Progress in Neural Information Processing. Berlin :Springer, 1996, 1207-1210.
[53] M. Herrmann, H. H. Yang. Perspectives and limitations of self-organizing maps in blind separation of source signals[C]. Progress in Neural Information Processing Systems: Proc. ICONIP’96, 1996, 1211– 1216.
[54] J. K. Lin, D. G. Grier, J. D. Cowan. Perspectives and limitations of self-organizing maps in blind separation of source SOM[C]. Advances in Neural Information Processing Systems. Cambridge, MA: MIT Press, Sep. 1997.
[55] P. Pajunen, A. Hyvarinen, J. Karhunen. Nonlinear blind source separation by self-organizing maps[C]. Progress in Neural InformationProcessing: Proc. ICONIP’96, 1996, 1211–1216.
[56] G. Burel. Blind separation of sources: A nonlinear neural algorithm[J]. Neural Networks, 1992, 5(6):937-947.
[57] H. H. Yang, S. Amari, A. Cichocki. Information-theoretic approach to blind separation of sources in nonlinear mixture[J]. Signal Processing, 1998, 64: 291-300.
[58] Y. Tan, J. Wang, J. M. Zurada. Nonlinear blind source separation using a radial basis function network[J]. IEEE Trans. Neural Networks, 2001, 12:124–134.
[59] F. J. Theis, W. E. Lang, C. G. Puntonet (2004). A geometric algorithm for overcomplete linear ICA[J]. Neurocomputing. 56:381-398.
[60] G.H. Xu, H. Liu, L. Tong, T. Kailath, A least-squares approach to blind channel identification[J]. IEEE Trans. Signal Processing, Dec. 1995, 43(12):2982-2993.
[61] Y.Q. Li, J. Wang, A. Cichocki, Blind source extraction from convolutive mixtures in ill-conditoned multi-input multi-output channels[J]. IEEE Trans. Circuits and Systems-I:regular papers, Sept. 2004, 51(9):1814-1822.
[62]汪军,何振亚,卷积混叠盲分离[J].电子学报,1997,25(7): 7-11。
[63] D. Yellin, E. Weinstein, Criteria for multichannel signal separation[J]. IEEE Trans. Signal processing, 1994, 42(8): 2158-2168.
[64] H.N. Thi, C. Jutten, Blind source separation for convolutive mixtures[J]. Signal Processing, 1995, 45(2):209-229.
[65] K. Tokkola, Blind separation of delayed sources based on information maximization[C]. in Proc of ICASSP, Atlanta: ICASSP, 1996, pp.3509-3512.
[66]谭丽丽,韦岗,多输入多输出盲解卷问题的最大熵解法[J].电子学报,2000,28(1):114-116。
[67] S. Choi, A. Cichocki, and S. Amari, Two spatiotemporal decorrelation learning algorithms and their application to multichannel blind deconvolution[C]. Proc. Int. Conf. Acoust., Speech, and Signal Processing, 1999, 1085--1088.
[68] T. W. Lee, A. J. Bell, and R. Lambert, Blind separation of delayed and convolved sources[M]. Advances in Neural Information Processing Systems9. Cambridge, MA: MIT Press, 1997, 758–764.
[69] L. Parra, C. Spence. Convolutive blind separation of non-stationary sources[J]. IEEE Trans. Speech and Audio Processing, May 2000, 8(3):320-327.
[70] A. Dapena, L. Castedo, A novel frequency domain approach for separating convolutive mixtures of temporally-white signals[J]. Digital Signal Processing, 2003, 13:301-316,
[71] Y. Zhou, B.L. Xu, Blind source separation in frequency domain[J]. Signal Processing, 2003, 83: 2037-2046.
[72] N. Mitianoudis, M.E. Davies, Audio Source Separation of Convolutive Mixtures[J]. IEEE Trans. Speech and Audio processing, September 2003, 11(5): 489-497.
[73] M.Z. Ikram, D.R. Morgan, Permutation inconsistency in blind speech separation: investigation and solutions[J]. IEEE Trans. Speech and Audio Processing, Jan. 2005, 13(1):1-13.
[74] Y. Sato, A method of self-recovering equalization for multilevel amplitude-modulation systems[J]. IEEE Trans. on Commun., 1975, 23 (6):679–682.
[75] D.N. Godard, Self-recovering equalization and carrier tracking in two-dimension data communication systems[J]. IEEE Trans on Commun, 1980, 28(11):1867–1875.
[76] A. Benveniste, M. Goursat, Blind Equalizers[J]. IEEE Trans on Commun, 1984, 32(8):871–883.
[77] S. Bellini, Bussgang Techniques for Blind Deconvolution and Blind Equalization[M]. Englewood Cliffs: Prentice-Hall, 1994.
[78] C. Platt, F. Faggin, Networks for the separation of sources that are superimposed and delayed[C]. Advances In Neural Information Processing Systems. 1991,730–737.
[79] T. Nomura, M. Eguchi, et al, An extension of the herault-jutten network to signal including delays for blind separation[C]. Proceedings of IEEE Workshop on Neural Networks for Signal Processing. Kyoto, 1996.
[80] D. Yellin, E. Wensten, Criteria for multichannel signal separation[J]. IEEE Trans. Signal Processsing, 1994, 42(8):2158–2168.
[81] L. Parra, C. Spence. Convolutive blind separation of non-stationarysources[J]. IEEE Trans. Speech and Audio Processing, May 2000, 8(3):320-327.
[82] K. Rahbar, J.P. Reilly, J.H. Manton, Blind identification of MIMO FIR systems driven by quasistationary sources using second-order statistics: a frequency domain approach[J]. IEEE Trans. Signal Processing, Feb. 2004, 52(2):406-417.
[83] R.M. Lambert, Multi-channel blind deconvolution: FIR Matrix Algebra and Separation of Multipath Mixtures[M]. Galifornia: University of Southern California, 1996.
[84] L. Parra, C. Spence. Convolutive blind separation of non-stationary sources[J]. IEEE Trans. Speech and Audio Processing, May 2000, 8(3):320-327.
[85] K. Rahbar, J.P. Reilly, J.H. Manton, Blind identification of MIMO FIR systems driven by quasistationary sources using second-order statistics: a frequency domain approach[J]. IEEE Trans. Signal Processing, Feb. 2004, 52(2):406-417.
[86] S. Haykin, Z. Chen. The cocktail party problem[J]. Neural computation, 2005, 17:1875-1902.
[87]章晋龙,实时线形混叠信号盲分离算法及其应用研究[D].博士学位论文,华南理工大学,2003年。
[88] A. Taleb. An algorithm for the blind identification of N independent signals with 2 sensors[C]. In Proc. 16th Int. Symp. on signal processing and its applications (ISSPA’01), Kuala-Lumpur, Malaysia, Aug. 13-16,2001,5-8.
[89] L. De Lathauwer, J. Castaing. Second order blind identification of undetermined mixtures[C]. In Proc. 6th Int. Conf. on Independent Component Analysis and Blind Source Separation (ICA 2006), Charleston, SC, USA, March 5-8, 2006.
[90] Di Persia L., Milone D., and Yanagida M. Indeterminacy Free Frequency-Domain Blind Separation of Reverberant Audio Sources[J]. IEEE Transactions on Audio Speech and Language Processing, 2009, 17 (2): 299-311.
[91] Cichocki A. and Amari S. Adaptive blind signal and image processing: learning algorithms and applications[M]. John Wiley & Sons, Ltd, 2002.
[92] Belouchrani A., AbedMeraim 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.
[93] Yeredor A. Blind source separation via the second characteristic function[J]. Signal Processing, 2000, 80 (5): 897-902.
[94] Ziehe A., Laskov P., Nolte G., and Muller 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: 777-800.
[95] Moreau E. A generalization of joint-diagonalization criteria for source separation[J]. IEEE Transactions on Signal Processing, 2001, 49 (3): 530-541.
[96] John M. and Rahbar K. joint diagonalization of correlation matrices by using newton methods with application to blind signal separation[J]. IEEE, Sensor Array and Multichannel Signal Processing Workshop Proceedings, 2002: 403-407.
[97] Wang F.X., Liu Z.K., and Zhang J. Nonorthogonal joint diagonalization algorithm based on trigonometric parameterization[J]. IEEE Transactions on Signal Processing, 2007, 55 (11): 5299-5308.
[98] Chabriel G., Barrere J., Thirion-Moreau N., and Moreau E. Algebraic Joint Zero-Diagonalization and Blind Sources Separation[J]. IEEE Trans Signal Processing, 2008, 56 (3): 980 - 989
[99] Wang F.X., Liu Z.K., and Zhang J. A new joint diagonalization algorithm with application in blind source separation[J]. IEEE Signal Processing Letters, 2006, 13 (1): 41-44.
[100] De Lathauwer L. and Castaing J. Blind Identification of Underdetermined Mixtures by Simultaneous Matrix Diagonalization[J]. IEEE Transactions on Signal Processing, 2008, 56 (3): 1096– 1105
[101] Chen B.N. and Petropulu A.P. Frequency domain blind MIMO system identification based on second- and higher order statistics[J]. IEEE Transactions on Signal Processing, 2001, 49 (8): 1677-1688.
[102] Sheinvald J. On blind beamforming for multiple non-Gaussian signals and the constant-modulus algorithm[J]. IEEE Transactions on Signal Processing, 1998, 46 (7): 1878-1885.
[103] Cardoso J.F. and Souloumiac A. Blind beamforming for non-Gaussiansignals[J]. Radar and Signal Processing, IEE Proceedings F, 1993, 140 (6): 362-370.
[104] Moreau E. and Comon P. Comments on blind beamforming for multiple non-gaussian signals and the constant-modulus algorithm[J]. IEEE Transactions on Signal Processing, 2000, 48 (11): 3248-3250.
[105] Fadaili E., Moreau N.T., and Moreau E. Nonorthogonal joint diagonalization/zero diagonalization for source separation based on time-frequency distributions[J]. IEEE Transactions on Signal Processing, 2007, 55 (5): 1673-1687.
[106] Cardoso J.F. On the performance of orthogonal source separation algorithms[C]. Proc. Europ. Assoc. Signal Process, Edinburgh, U.K., 1994 VII.
[107] 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.
[108] 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.
[109] Vollgraf R. and Obermayer K. Quadratic optimization for simultaneous matrix diagonalization[J]. IEEE Transactions on Signal Processing, 2006, 54 (9): 3270-3278.
[110] 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.
[111] Zhou G.X., Yang Z.Y., Wu Z.Z., and Zhang J.L. Non-orthogonal joint diagonalization with diagonal constraints[J]. Progress in Natural Science, 2008, 18 (6): 735-739.
[112] 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.
[113] Degerine S. and Kane E. A Comparative Study of Approximate Joint Diagonalization Algorithms for Blind Source Separation in Presence of Additive Noise[J]. IEEE Transactions on Signal Processing, 2007, 55 (6, Part 2): 3022-3031.
[114] Pham D.T. and Cardoso J.F. Blind separation of instantaneous mixtures of nonstationary sources[J]. IEEE Transactions on Signal Processing, 2001, 49 (9): 1837-1848.
[115] Vollgraf R. and Obermayer K. Quadratic optimization for simultaneous matrix diagonalization[J]. IEEE Transactions on Signal Processing, 2006, 54 (9): 3270-3278.
[116] Xie S.L., He Z.S., and Fu Y.L. A note on Stone's conjecture of blind signal separation[J]. Neural Computation, 2005, 17 (2): 321-330.
[117] John M. and Rahbar K. joint diagonalization of correlation matrices by using newton methods with application to blind signal separation[C]. IEEE, Sensor Array and Multichannel Signal Processing Workshop Proceedings, 2002: 403-407.
[118] 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.
[119] Cichocki A., Amari S., Siwek K., and Tanaka T., ICALABA toolboxes. (March 28, 2007.). [OnLine]. Available: http://www.bsp.brain.riken.jp/ICALAB.
[120] Belouchrani A., AbedMeraim 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.
[121] Luenberger D.G. Linear and Nonlinear Programming [M]. 2nd ed: Kluwer Academic Pub, 2003: 491.
[122] A. Belouchrani, J.F. Cardoso, Maximum likelihood source separation for discrete sources[C]. Proc. EUSIPCO, 1994, 768-771.
[123] M. Zibulevsky, B.A. Pearlmutter, Blind source separation by sparse decomposition in a signal dictionary[J]. Neural computation, April 2001, 13(4): 863-882.
[124] P. Bofill, M. Zibulevsky, Underdetermined source separation using sparse representation[J]. Signal processing, 2001, 81: 2353-2362.
[125] Zhaoshui He, Shengli Xie, Yuli Fu, Sparse representation and blind source separation of ill-posed mixtures[J]. Science in China Series F-Information Science
[126] Yuanqing Li, Amari, S., Cichocki, A., Ho, D.W.C., Shengli Xie, Underdetermined blind source separation based on sparserepresentation[J]. IEEE Transactions on Signal Processing, February 2006, 54(2): 423-437
[127] He Zhaoshui, Xie Shengli, Fu Yuli, Sparsity analysis of signals[J]. Progress in Natural Science, 16(9): 117-122, 2006.
[128] Li, Y., Wang, J., Zurada, J.M.: Blind extraction of singularly mixed source signals[J]. IEEE Transactions on Neural Networks, 2000, 11(6):1413– 1422.
[129] Pando Georiev, Fabian Theis, Andrzej Cichocki, Sparse component analysis and blind separation of underdetermined mixtures[J]. IEEE Transactions of Neural Networks, July 2005, 16(4).
[130] P. G. Georgiev, F. J. Theis, and A. Cichocki. Blind source separation and sparse component analysis of overcomplete mixtures[C]. Proceedings of International Conference on Acoustics, Speech, and Signal Processing (ICASSP2004), Montreal, Canada, May 2004, IEEE Signal Processing Society, V: 493–496.
[131] Z. He, A. Cichocki. K-Subspace Clustering and its Application in Sparse Component Analysis[C]. The 14th European Symposium on Artificial Neural Networks, ESANN-2006 Bruges (Belgium), April 26-28, 2006
[132]何昭水,谢胜利,傅予力。信号的稀疏性分析[J].自然科学进展,2006, 16(9):1167-1173。
[133] A. Cichocki and S. Amari, Adaptive blind signal and image processing: learning algorithms and applications[M]. New York: Wiley, 2002.
[134] J. F. Cardoso, Blind signal separation: statistical principles[C]. Proc. IEEE (Special Issue on Blind Identification and Estimation) , Oct. 1998, 90: 2009–2026.
[135] P. Comon, Independent component analysis, a new concept? [J]. Signal Process, 1994, 36: 287–314.
[136] M. Girolami, Self-Organizing Neural Networks--Independent Component Analysis and Blind Source Separation[M]. New York: Springer-Verlag, 1999.
[137] M. Zibulevsky, B. A. Pearlmutter, Blind source separation by sparse decomposition in a signal dictionary[J]. Neural Computation, 2001, 13: 863-882
[138] 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 Letter, 1999, 6(4): 87-90.
[139] K. K. Delgado, J. F. Murray, K. Engan, T. W. Lee, and T. J. Sejnowski, Dictionary learning algorithms for sparse representation[J]. Neural Computation, 2003, 15:349-396
[140] P. Bofill, M. Zibulevsky, Underdetermined blind source separation using sparse representations[J]. Signal Processing. 2001,81: 2353-2362
[141] Y. Q. Li, C. Andrzej, S. Amari. Analysis of sparse representation and blind source separation[J]. Neural Computation. 2004 16:1193-1234.
[142] M. Zibulevsky, P. Kisilev, Y. Y. Zeevi, and B. A. Pearlmutter, Blindsource separation via mutinode sparse representation[M]. In T. K. Leen, T. G. Dietterich, & V. Tresp (Eds.), Advances in neural information processing system, 13. Cambridge, MA: MIT Press. 2001.
[143] F. J. Theis, W. E. Lang, C. G. Puntonet, A geometric algorithm for overcomplete linear ICA[J]. Neurocomputing,2004,56: 381-398.
[144] M. Xiao, S. L. Xie, Y. L. Fu. A novel approach for Underdetermined Blind speech signal Separation [C]. DCDIS 2005.
[145] M. Xiao, S. L. Xie, Y. L. Fu. A searching-and-averaging-based method for underdetermined blind speech signals separation in time domain[J]. Science in China Series E-Technological Sciences, 2007
[146] I. Takigawa, M. Kudo, and J. Toyama, Perfoamance analysis of minimum l1-norm solution for underdetermined source separation[J]. IEEE Trans on Signal Processing, 2004, 52 (3): 582-591
[147] D. L. Donoho, On minimum entropy segmentation[M]. In C. Chui, L. Montefusco, & Lm Puccio (Eds.), wavelets: Theory.algorithms, and applications (pp.233-269).San Diego, CA: Academic Press.1994
[148] K. K. Delgado, J. F. Murray, K. Engan, T. W. Lee, and T. J. Sejnowski, Dictionary learning algorithms for sparse representation[J]. Neural Computation, 2003, 15: 349-396.
[149] D. L. Donoho and M. Elad, Maximal sparsity representation via l1 minimization [J]. Proc. Nat. Aca. Sci. , 2003, 100: 2197-2202
[150] P. G. Georgiev, F. J. Theis, A. Cichocki. Sparse component analysis and blind source separation of underdetermined mixtures[J]. IEEETransactions of Neural Networks. 2005, 16(4):992-996.
[151] O. Yilmaz, S. Rickard. Blind separation of speech mixtures via time-frequency masking[J]. IEEE Trans. on signal processing. 2004,52( 7): 1830-1847.
[152] F. Abrard, Y. A. Deville. Time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources[J]. Signal processing,2005,85(7):1389-1403
[153] M. Xiao, S. Xie, & Y. Fu. Searching-and-averaging method of underdetermined blind speech signal separation in time domain[J]. Sci China Ser F-Inf Sci, 2007, 50(5):771-782,
[154]李荣华,盲信号分离的优化算法及其应用[D].博士学位论文,2008
[155]肖明,谢胜利,傅予力.基于频域单源区间的具有延迟的欠定盲分离[J].电子学报,2007, 35(12): 2279-2283.
[156]康浔,肖明.频域单源区间和欠定情况下的盲信号分离[J].计算机工程,2009, 35(12): 269-271
[157] G. X. Zhou, Z. Y. Yang, Z. Z. Wu, and J. L. Zhang, Non-orthogonal joint diagonalization with diagonal constraints, Progress in Natural Science, 2008, 18(6): 735-739.
[158]谭北海,谢胜利,基于源信号数目估计的欠定盲分离,电子与信息学报,2008,30(4):863-867
[159]谢胜利,何昭水,高鹰,信号处理的自适应理论[M].科学出版社,2006。
[160]余英林,谢胜利,蔡汉添,信号处理新方法导论[M].清华大学出版社,2004
[2] A. Hyvarinen, E. Oja, Independent component analysis: algorithms and applications[J]. Neural Networks, June 2000, 13(4-5):411-430.
[3] A. Cichocki, S. Amari, Adaptive blind signal and image processing: learning algorithms and applications[M] John Wiley and Sons, LTD, June 2002.
[4] H. Sahlin, H. Broman, Separation of real-world signals[J]. Signal Processing, 1998, 64(2): 103-113.
[5] J. Joutsensalo and P.Pajunen. Blind Symbol Learning Algorithms for CDMA System[C]. Int Joint Conf. On Neural Networks, (IJCNN’98), Anchorage, Alaska, May 4-9,1998, 1:152-155.
[6] J. Joutsensalo and Ristaniemi, Blind Multi-User Detection by Fast Fixed Point Algorithm without Prior Knowledge of Symbol-Level Timing[C]. Proc. IEEE Signal Processing Workshop on Higher Order Statistics, Ceasarea, Israel, June 14-16, 1999, 305-308.
[7] T. Ristaniemi and J. Joutsensalo, Independent component analysis with code information utilization in DS-CDMA signal separation[C]. Proc. IEEE GLOBECOM’99, Riode Janeiro, Brazil, December 5-9, 1999, 1a: 320-324.
[8] R. Cristescu, J. Joutsensalo and T. Ristaniemi, Fading ChannelEstimation by Mutual Information Minimization for Gaussian Stochastic Processes[C]. Proc. IEEE International Conference on Communications, New Orleans, LA, 18-22 June, 2000:56-59.
[9] S. Talwar, M. Viberg, and A. Paulraj. Blind estimation of multiple co-channel digital signals using an antenna array[J]. IEEE Signal Processing Letters, February 1994, 1(2):29–31.
[10] S. Talwar, M. Viberg, and A. Paulraj. Blind estimation of synchronous co-channel digital signals using an antenna array. Part I: Algorithms[J]. IEEE Trans. Signal Processing, May 1996, 44(5): 1184–1197.
[11]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.
[12]倪晋平,马远良等,用独立分量分析算法实现水声信号盲分离[J],声学学报,2002,27(4):321-326.
[13]张安清,章新华,基于信息理论的舰船噪声盲分离算法[J],系统工程与电子技术,2002,24(1):38-41.
[14] Y. Feng, V. Zarzoso, A.K. Nandi, WDM monitoring through blind signal separation[C]. Optical Fiber Communication Conference and Exhibit, 2002. OFC 2002, 17-22 March 2002, 746-748.
[15] Y.M. Feng; V. Zarzoso, A.K. Nandi, WDM monitoring using blind signal separation based on higher-order statistics[C]. 14th International Conference on Digital Signal Processing, July 2002, 1:1-3.
[16]斯华龄,张立明,智能视觉图像处理,上海:上海科技教育出版社,2002年10月第1版。
[17] S. Choi, A. Cichocki, H. M. Park, et al. Blind source separation and independent component analysis: A review. Neural Information Processing - Letters and Reviews[J]. January 2005, 6(1):1-57
[18] L. Molgedey, H.G. Schuster. Separation of a mixture of independent signals using time delayed correlations[J].Physical Review Letters, 1994,72(23):3634-3637.
[19] A. Beloouchrani, A.M. Karim, J.F. Cardoso, et al. A blind source separation technique using second-order statistics[J]. IEEE Trans. Signal Process, 1997,45 (2):434-443.
[20] A. Ziehe, K. R.M¨uller, G. Nolte, et al. Artifact reduction in biomagnetic recordings based on time-delayed second order correlations[J]. IEEE Trans. on Biomedical Engineering, 2000, 47: 75-87.
[21] S. Choi, A. Cichocki, L. Zhang, et al. Approximate maximum likelihood source separation using the natural gradient[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, January 2003, E86-A(1):198-205.
[22] A. Cichocki, A. Belouchrani. Sources separation of temporally correlated sources from noisy data using bank of band-pass filters[C]. In Third International Conference on Independent Component Analysis and Signal Separation (ICA-2001), San Diego, USA, Dec. 2001, 173-178.
[23] K. Matsuoka, M. Ohya, M. Kawamoto. A neural net for blind separationof nonstationary signals[J].Neural Networks, 1995, 8(3):411-419.
[24] S. Choi, A. Cichocki, A. Belouchrani. Second order nonstationary source separation[J]. Journal of VLSI Signal Processing,August 2002, 32(1–2):93-104.
[25] L. Parra, C. Spence. Convolutive blind source separation of non-stationary sources[J]. IEEE Trans. Speech and Audio Processing, May 2000,8(3):320-327.
[26] A. Belouchrani, M.G. Amin. A new approach for blind source separation using time-frequency distributions[J].Proc. SPIE, 1996, 2846:193-203.
[27] O. Yilmaz, S. Rickard. Blind separation of speech mixtures via time-frequency masking[J]. IEEE trans on signal processing. 52(7): 1830-1847.
[28] F. Abrard, Y. A. Deville. Time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources[J]. Signal processing 2005,85:1389-1403
[29] S. Rickard, T. Melia, C. Fearon. DESPRIT - histogram based blind source separation of more sources than sensors using subspace methods[C]. Proceedings of the IEEE Workshop on Applications of Signal Processing in Audio and Acoustics, New Paltz, NY, USA, October 2005, 5-8.
[30] T. Melia, S. Rickard, C. Fearon. Extending the DUET blind source separation technique[C]. Proceedings of Signal Processing with Adaptative Sparse Structured Representations Workshop (SPARS '05), Rennes, France, November 2005.
[31] K. R. M¨uller, P. Philips, A. Ziehe. JADETD: Combining higher-order statistics and temporal information for blind source separation (with noise)[C]. Proc. ICA’99, Aussois, France, 1999,87-92.
[32] A. Belouchrani. Separation Autodidacte de Sources: Algorithme, Performances et Application a des Signaux Exp′erimentaux[D]. PhD thesis, ENST, Telecom Paris, July 1995.
[33] A. Cichocki, S. Amari. Adaptive blind signal and image processing: learning algorithms and applications[M].John Wiley and Sons, LTD, June 2002.
[34] L. Tong, R. Liu, V.C. Soon, et al, Indeterminacy and identifiability of blind identification[J]. IEEE Trans on Circuits and systems, 1991, vol. 38(5):499-506.
[35] A. Belouchrani, K. Abed-Meraim, J. F. Cardoso, et al. A blind source separation techniqueusing second-order statistics[J]. IEEE Trans. Signal Processing, February 1997, 45(2): 434–444.
[36] G. H. Golub, C. F. Van Loan. Matrix Computations[J]. 2nd edition. Johns Hopkins, 1993.
[37] J. F. Cardoso. Jacobi angles for simultaneous diagonalization[J]. SIAM J. Mat. Anal. Appl, 1996, 17(1): 161–164.
[38] D. T. Pham. Joint approximate diagonalization of positive definite hermitian matrices[C]. Technical Report LMC/IMAG, University of Grenoble, France, 2000.
[39] Y.Q. Li, J. Wang, J.M. Zurada, Blind extraction of singularly mixedsource signals[J]. IEEE Trans on Neural Networks, 2000, 11(6):1413-1422.
[40] Y.Q. Li, J. Wang, Sequential blind extraction of instantaneously mixed sources[J]. IEEE Trans. Signal processing, May 2002, 50(5): 997-1006.
[41] A. Belouchrani, J.F. Cardoso, Maximum likelihood source separation for discrete sources[C]. in Proc. EUSIPCO, 1994, 768-771.
[42] M. Zibulevsky, B.A. Pearlmutter, Blind source separation by sparse decomposition in a signal dictionary[J]. Neural computation, April 2001, 13(4): 863-882.
[43] T. W. Lee, M.S. Lewicki, M. Girolami, T.J. Sejnowski, Blind source separation of more sources than mixtures using overcomplete representation[J]. IEEE Signal processing letter, 1999, 6(4): 87-90.
[44] M.S. Lewicki, T.J. Sejnowski, Learning overcomplete representations[J]. Neural computation, 2000, 12:337-365.
[45] Y.Q. Li, A. Cichocki, S. Amari, Analysis of sparse representation and blind source separation[J]. Neural computation, June 2004, 16(6): 1193-1234.
[46] P. Bofill, M. Zibulevsky, Underdetermined source separation using sparse representation[J]. Signal processing, 2001, 81: 2353-2362.
[47] B.A. Pearlmutter, V.K. Potluru, Sparse separation: Principles and tricks[C]. Proc SPIE "Independent Component Analyses, Wavelets, and Neural Networks", April 2003, 5102:1-4.
[48] I.F. Gorodnitsky and B.D. Rao. Sparse signal reconstruction fromlimited data using FOCUSS: A recursive weighted minimum norm algorithm[J]. IEEE Trans. SP, 1997, 45(3): 600-616.
[49] S.F. Cotter, B.D. Rao, K. Engan et al. Sparse solutions to linear inverse problems with multiple measurement vectors[J]. IEEE Trans. Signal Processing, 2005, 53(7): 2477–2488.
[50] A. Taleb, C. S. Jutten, A. Xichocki. Information back-propagation for blind separation of sources from non-linear mixtures: An entropy-based algorithm[C]. in Proc of ICASSP. Washinton, ICASSP, 1998, 2089-2092.
[51] A. Taleb, C. Jutten. Source separation in post-nonlinear mixtures[J]. IEEE Trans. Signal Processing, October 1999, 47 (10):2807-2820.
[52] P. Pahybeb, A. Hyvarinen, J. Karhunen. Nonlinear blind source separation by self-organizating maps[C]. Progress in Neural Information Processing. Berlin :Springer, 1996, 1207-1210.
[53] M. Herrmann, H. H. Yang. Perspectives and limitations of self-organizing maps in blind separation of source signals[C]. Progress in Neural Information Processing Systems: Proc. ICONIP’96, 1996, 1211– 1216.
[54] J. K. Lin, D. G. Grier, J. D. Cowan. Perspectives and limitations of self-organizing maps in blind separation of source SOM[C]. Advances in Neural Information Processing Systems. Cambridge, MA: MIT Press, Sep. 1997.
[55] P. Pajunen, A. Hyvarinen, J. Karhunen. Nonlinear blind source separation by self-organizing maps[C]. Progress in Neural InformationProcessing: Proc. ICONIP’96, 1996, 1211–1216.
[56] G. Burel. Blind separation of sources: A nonlinear neural algorithm[J]. Neural Networks, 1992, 5(6):937-947.
[57] H. H. Yang, S. Amari, A. Cichocki. Information-theoretic approach to blind separation of sources in nonlinear mixture[J]. Signal Processing, 1998, 64: 291-300.
[58] Y. Tan, J. Wang, J. M. Zurada. Nonlinear blind source separation using a radial basis function network[J]. IEEE Trans. Neural Networks, 2001, 12:124–134.
[59] F. J. Theis, W. E. Lang, C. G. Puntonet (2004). A geometric algorithm for overcomplete linear ICA[J]. Neurocomputing. 56:381-398.
[60] G.H. Xu, H. Liu, L. Tong, T. Kailath, A least-squares approach to blind channel identification[J]. IEEE Trans. Signal Processing, Dec. 1995, 43(12):2982-2993.
[61] Y.Q. Li, J. Wang, A. Cichocki, Blind source extraction from convolutive mixtures in ill-conditoned multi-input multi-output channels[J]. IEEE Trans. Circuits and Systems-I:regular papers, Sept. 2004, 51(9):1814-1822.
[62]汪军,何振亚,卷积混叠盲分离[J].电子学报,1997,25(7): 7-11。
[63] D. Yellin, E. Weinstein, Criteria for multichannel signal separation[J]. IEEE Trans. Signal processing, 1994, 42(8): 2158-2168.
[64] H.N. Thi, C. Jutten, Blind source separation for convolutive mixtures[J]. Signal Processing, 1995, 45(2):209-229.
[65] K. Tokkola, Blind separation of delayed sources based on information maximization[C]. in Proc of ICASSP, Atlanta: ICASSP, 1996, pp.3509-3512.
[66]谭丽丽,韦岗,多输入多输出盲解卷问题的最大熵解法[J].电子学报,2000,28(1):114-116。
[67] S. Choi, A. Cichocki, and S. Amari, Two spatiotemporal decorrelation learning algorithms and their application to multichannel blind deconvolution[C]. Proc. Int. Conf. Acoust., Speech, and Signal Processing, 1999, 1085--1088.
[68] T. W. Lee, A. J. Bell, and R. Lambert, Blind separation of delayed and convolved sources[M]. Advances in Neural Information Processing Systems9. Cambridge, MA: MIT Press, 1997, 758–764.
[69] L. Parra, C. Spence. Convolutive blind separation of non-stationary sources[J]. IEEE Trans. Speech and Audio Processing, May 2000, 8(3):320-327.
[70] A. Dapena, L. Castedo, A novel frequency domain approach for separating convolutive mixtures of temporally-white signals[J]. Digital Signal Processing, 2003, 13:301-316,
[71] Y. Zhou, B.L. Xu, Blind source separation in frequency domain[J]. Signal Processing, 2003, 83: 2037-2046.
[72] N. Mitianoudis, M.E. Davies, Audio Source Separation of Convolutive Mixtures[J]. IEEE Trans. Speech and Audio processing, September 2003, 11(5): 489-497.
[73] M.Z. Ikram, D.R. Morgan, Permutation inconsistency in blind speech separation: investigation and solutions[J]. IEEE Trans. Speech and Audio Processing, Jan. 2005, 13(1):1-13.
[74] Y. Sato, A method of self-recovering equalization for multilevel amplitude-modulation systems[J]. IEEE Trans. on Commun., 1975, 23 (6):679–682.
[75] D.N. Godard, Self-recovering equalization and carrier tracking in two-dimension data communication systems[J]. IEEE Trans on Commun, 1980, 28(11):1867–1875.
[76] A. Benveniste, M. Goursat, Blind Equalizers[J]. IEEE Trans on Commun, 1984, 32(8):871–883.
[77] S. Bellini, Bussgang Techniques for Blind Deconvolution and Blind Equalization[M]. Englewood Cliffs: Prentice-Hall, 1994.
[78] C. Platt, F. Faggin, Networks for the separation of sources that are superimposed and delayed[C]. Advances In Neural Information Processing Systems. 1991,730–737.
[79] T. Nomura, M. Eguchi, et al, An extension of the herault-jutten network to signal including delays for blind separation[C]. Proceedings of IEEE Workshop on Neural Networks for Signal Processing. Kyoto, 1996.
[80] D. Yellin, E. Wensten, Criteria for multichannel signal separation[J]. IEEE Trans. Signal Processsing, 1994, 42(8):2158–2168.
[81] L. Parra, C. Spence. Convolutive blind separation of non-stationarysources[J]. IEEE Trans. Speech and Audio Processing, May 2000, 8(3):320-327.
[82] K. Rahbar, J.P. Reilly, J.H. Manton, Blind identification of MIMO FIR systems driven by quasistationary sources using second-order statistics: a frequency domain approach[J]. IEEE Trans. Signal Processing, Feb. 2004, 52(2):406-417.
[83] R.M. Lambert, Multi-channel blind deconvolution: FIR Matrix Algebra and Separation of Multipath Mixtures[M]. Galifornia: University of Southern California, 1996.
[84] L. Parra, C. Spence. Convolutive blind separation of non-stationary sources[J]. IEEE Trans. Speech and Audio Processing, May 2000, 8(3):320-327.
[85] K. Rahbar, J.P. Reilly, J.H. Manton, Blind identification of MIMO FIR systems driven by quasistationary sources using second-order statistics: a frequency domain approach[J]. IEEE Trans. Signal Processing, Feb. 2004, 52(2):406-417.
[86] S. Haykin, Z. Chen. The cocktail party problem[J]. Neural computation, 2005, 17:1875-1902.
[87]章晋龙,实时线形混叠信号盲分离算法及其应用研究[D].博士学位论文,华南理工大学,2003年。
[88] A. Taleb. An algorithm for the blind identification of N independent signals with 2 sensors[C]. In Proc. 16th Int. Symp. on signal processing and its applications (ISSPA’01), Kuala-Lumpur, Malaysia, Aug. 13-16,2001,5-8.
[89] L. De Lathauwer, J. Castaing. Second order blind identification of undetermined mixtures[C]. In Proc. 6th Int. Conf. on Independent Component Analysis and Blind Source Separation (ICA 2006), Charleston, SC, USA, March 5-8, 2006.
[90] Di Persia L., Milone D., and Yanagida M. Indeterminacy Free Frequency-Domain Blind Separation of Reverberant Audio Sources[J]. IEEE Transactions on Audio Speech and Language Processing, 2009, 17 (2): 299-311.
[91] Cichocki A. and Amari S. Adaptive blind signal and image processing: learning algorithms and applications[M]. John Wiley & Sons, Ltd, 2002.
[92] Belouchrani A., AbedMeraim 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.
[93] Yeredor A. Blind source separation via the second characteristic function[J]. Signal Processing, 2000, 80 (5): 897-902.
[94] Ziehe A., Laskov P., Nolte G., and Muller 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: 777-800.
[95] Moreau E. A generalization of joint-diagonalization criteria for source separation[J]. IEEE Transactions on Signal Processing, 2001, 49 (3): 530-541.
[96] John M. and Rahbar K. joint diagonalization of correlation matrices by using newton methods with application to blind signal separation[J]. IEEE, Sensor Array and Multichannel Signal Processing Workshop Proceedings, 2002: 403-407.
[97] Wang F.X., Liu Z.K., and Zhang J. Nonorthogonal joint diagonalization algorithm based on trigonometric parameterization[J]. IEEE Transactions on Signal Processing, 2007, 55 (11): 5299-5308.
[98] Chabriel G., Barrere J., Thirion-Moreau N., and Moreau E. Algebraic Joint Zero-Diagonalization and Blind Sources Separation[J]. IEEE Trans Signal Processing, 2008, 56 (3): 980 - 989
[99] Wang F.X., Liu Z.K., and Zhang J. A new joint diagonalization algorithm with application in blind source separation[J]. IEEE Signal Processing Letters, 2006, 13 (1): 41-44.
[100] De Lathauwer L. and Castaing J. Blind Identification of Underdetermined Mixtures by Simultaneous Matrix Diagonalization[J]. IEEE Transactions on Signal Processing, 2008, 56 (3): 1096– 1105
[101] Chen B.N. and Petropulu A.P. Frequency domain blind MIMO system identification based on second- and higher order statistics[J]. IEEE Transactions on Signal Processing, 2001, 49 (8): 1677-1688.
[102] Sheinvald J. On blind beamforming for multiple non-Gaussian signals and the constant-modulus algorithm[J]. IEEE Transactions on Signal Processing, 1998, 46 (7): 1878-1885.
[103] Cardoso J.F. and Souloumiac A. Blind beamforming for non-Gaussiansignals[J]. Radar and Signal Processing, IEE Proceedings F, 1993, 140 (6): 362-370.
[104] Moreau E. and Comon P. Comments on blind beamforming for multiple non-gaussian signals and the constant-modulus algorithm[J]. IEEE Transactions on Signal Processing, 2000, 48 (11): 3248-3250.
[105] Fadaili E., Moreau N.T., and Moreau E. Nonorthogonal joint diagonalization/zero diagonalization for source separation based on time-frequency distributions[J]. IEEE Transactions on Signal Processing, 2007, 55 (5): 1673-1687.
[106] Cardoso J.F. On the performance of orthogonal source separation algorithms[C]. Proc. Europ. Assoc. Signal Process, Edinburgh, U.K., 1994 VII.
[107] 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.
[108] 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.
[109] Vollgraf R. and Obermayer K. Quadratic optimization for simultaneous matrix diagonalization[J]. IEEE Transactions on Signal Processing, 2006, 54 (9): 3270-3278.
[110] 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.
[111] Zhou G.X., Yang Z.Y., Wu Z.Z., and Zhang J.L. Non-orthogonal joint diagonalization with diagonal constraints[J]. Progress in Natural Science, 2008, 18 (6): 735-739.
[112] 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.
[113] Degerine S. and Kane E. A Comparative Study of Approximate Joint Diagonalization Algorithms for Blind Source Separation in Presence of Additive Noise[J]. IEEE Transactions on Signal Processing, 2007, 55 (6, Part 2): 3022-3031.
[114] Pham D.T. and Cardoso J.F. Blind separation of instantaneous mixtures of nonstationary sources[J]. IEEE Transactions on Signal Processing, 2001, 49 (9): 1837-1848.
[115] Vollgraf R. and Obermayer K. Quadratic optimization for simultaneous matrix diagonalization[J]. IEEE Transactions on Signal Processing, 2006, 54 (9): 3270-3278.
[116] Xie S.L., He Z.S., and Fu Y.L. A note on Stone's conjecture of blind signal separation[J]. Neural Computation, 2005, 17 (2): 321-330.
[117] John M. and Rahbar K. joint diagonalization of correlation matrices by using newton methods with application to blind signal separation[C]. IEEE, Sensor Array and Multichannel Signal Processing Workshop Proceedings, 2002: 403-407.
[118] 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.
[119] Cichocki A., Amari S., Siwek K., and Tanaka T., ICALABA toolboxes. (March 28, 2007.). [OnLine]. Available: http://www.bsp.brain.riken.jp/ICALAB.
[120] Belouchrani A., AbedMeraim 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.
[121] Luenberger D.G. Linear and Nonlinear Programming [M]. 2nd ed: Kluwer Academic Pub, 2003: 491.
[122] A. Belouchrani, J.F. Cardoso, Maximum likelihood source separation for discrete sources[C]. Proc. EUSIPCO, 1994, 768-771.
[123] M. Zibulevsky, B.A. Pearlmutter, Blind source separation by sparse decomposition in a signal dictionary[J]. Neural computation, April 2001, 13(4): 863-882.
[124] P. Bofill, M. Zibulevsky, Underdetermined source separation using sparse representation[J]. Signal processing, 2001, 81: 2353-2362.
[125] Zhaoshui He, Shengli Xie, Yuli Fu, Sparse representation and blind source separation of ill-posed mixtures[J]. Science in China Series F-Information Science
[126] Yuanqing Li, Amari, S., Cichocki, A., Ho, D.W.C., Shengli Xie, Underdetermined blind source separation based on sparserepresentation[J]. IEEE Transactions on Signal Processing, February 2006, 54(2): 423-437
[127] He Zhaoshui, Xie Shengli, Fu Yuli, Sparsity analysis of signals[J]. Progress in Natural Science, 16(9): 117-122, 2006.
[128] Li, Y., Wang, J., Zurada, J.M.: Blind extraction of singularly mixed source signals[J]. IEEE Transactions on Neural Networks, 2000, 11(6):1413– 1422.
[129] Pando Georiev, Fabian Theis, Andrzej Cichocki, Sparse component analysis and blind separation of underdetermined mixtures[J]. IEEE Transactions of Neural Networks, July 2005, 16(4).
[130] P. G. Georgiev, F. J. Theis, and A. Cichocki. Blind source separation and sparse component analysis of overcomplete mixtures[C]. Proceedings of International Conference on Acoustics, Speech, and Signal Processing (ICASSP2004), Montreal, Canada, May 2004, IEEE Signal Processing Society, V: 493–496.
[131] Z. He, A. Cichocki. K-Subspace Clustering and its Application in Sparse Component Analysis[C]. The 14th European Symposium on Artificial Neural Networks, ESANN-2006 Bruges (Belgium), April 26-28, 2006
[132]何昭水,谢胜利,傅予力。信号的稀疏性分析[J].自然科学进展,2006, 16(9):1167-1173。
[133] A. Cichocki and S. Amari, Adaptive blind signal and image processing: learning algorithms and applications[M]. New York: Wiley, 2002.
[134] J. F. Cardoso, Blind signal separation: statistical principles[C]. Proc. IEEE (Special Issue on Blind Identification and Estimation) , Oct. 1998, 90: 2009–2026.
[135] P. Comon, Independent component analysis, a new concept? [J]. Signal Process, 1994, 36: 287–314.
[136] M. Girolami, Self-Organizing Neural Networks--Independent Component Analysis and Blind Source Separation[M]. New York: Springer-Verlag, 1999.
[137] M. Zibulevsky, B. A. Pearlmutter, Blind source separation by sparse decomposition in a signal dictionary[J]. Neural Computation, 2001, 13: 863-882
[138] 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 Letter, 1999, 6(4): 87-90.
[139] K. K. Delgado, J. F. Murray, K. Engan, T. W. Lee, and T. J. Sejnowski, Dictionary learning algorithms for sparse representation[J]. Neural Computation, 2003, 15:349-396
[140] P. Bofill, M. Zibulevsky, Underdetermined blind source separation using sparse representations[J]. Signal Processing. 2001,81: 2353-2362
[141] Y. Q. Li, C. Andrzej, S. Amari. Analysis of sparse representation and blind source separation[J]. Neural Computation. 2004 16:1193-1234.
[142] M. Zibulevsky, P. Kisilev, Y. Y. Zeevi, and B. A. Pearlmutter, Blindsource separation via mutinode sparse representation[M]. In T. K. Leen, T. G. Dietterich, & V. Tresp (Eds.), Advances in neural information processing system, 13. Cambridge, MA: MIT Press. 2001.
[143] F. J. Theis, W. E. Lang, C. G. Puntonet, A geometric algorithm for overcomplete linear ICA[J]. Neurocomputing,2004,56: 381-398.
[144] M. Xiao, S. L. Xie, Y. L. Fu. A novel approach for Underdetermined Blind speech signal Separation [C]. DCDIS 2005.
[145] M. Xiao, S. L. Xie, Y. L. Fu. A searching-and-averaging-based method for underdetermined blind speech signals separation in time domain[J]. Science in China Series E-Technological Sciences, 2007
[146] I. Takigawa, M. Kudo, and J. Toyama, Perfoamance analysis of minimum l1-norm solution for underdetermined source separation[J]. IEEE Trans on Signal Processing, 2004, 52 (3): 582-591
[147] D. L. Donoho, On minimum entropy segmentation[M]. In C. Chui, L. Montefusco, & Lm Puccio (Eds.), wavelets: Theory.algorithms, and applications (pp.233-269).San Diego, CA: Academic Press.1994
[148] K. K. Delgado, J. F. Murray, K. Engan, T. W. Lee, and T. J. Sejnowski, Dictionary learning algorithms for sparse representation[J]. Neural Computation, 2003, 15: 349-396.
[149] D. L. Donoho and M. Elad, Maximal sparsity representation via l1 minimization [J]. Proc. Nat. Aca. Sci. , 2003, 100: 2197-2202
[150] P. G. Georgiev, F. J. Theis, A. Cichocki. Sparse component analysis and blind source separation of underdetermined mixtures[J]. IEEETransactions of Neural Networks. 2005, 16(4):992-996.
[151] O. Yilmaz, S. Rickard. Blind separation of speech mixtures via time-frequency masking[J]. IEEE Trans. on signal processing. 2004,52( 7): 1830-1847.
[152] F. Abrard, Y. A. Deville. Time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources[J]. Signal processing,2005,85(7):1389-1403
[153] M. Xiao, S. Xie, & Y. Fu. Searching-and-averaging method of underdetermined blind speech signal separation in time domain[J]. Sci China Ser F-Inf Sci, 2007, 50(5):771-782,
[154]李荣华,盲信号分离的优化算法及其应用[D].博士学位论文,2008
[155]肖明,谢胜利,傅予力.基于频域单源区间的具有延迟的欠定盲分离[J].电子学报,2007, 35(12): 2279-2283.
[156]康浔,肖明.频域单源区间和欠定情况下的盲信号分离[J].计算机工程,2009, 35(12): 269-271
[157] G. X. Zhou, Z. Y. Yang, Z. Z. Wu, and J. L. Zhang, Non-orthogonal joint diagonalization with diagonal constraints, Progress in Natural Science, 2008, 18(6): 735-739.
[158]谭北海,谢胜利,基于源信号数目估计的欠定盲分离,电子与信息学报,2008,30(4):863-867
[159]谢胜利,何昭水,高鹰,信号处理的自适应理论[M].科学出版社,2006。
[160]余英林,谢胜利,蔡汉添,信号处理新方法导论[M].清华大学出版社,2004
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |