盲信号分离算法的研究
|
摘要
盲信号分离技术是现代信号处理领域的一个新的研究热点。目前，盲信号处理技术可以被应用于语音信号处理，图像信号处理，通讯信号处理，水声信号处理，医学信号处理以及数据挖掘等诸多领域。也正因为盲信号分离技术具有如此广阔的应用前景，盲信号分离问题从开始到现在的二十多年的时间内，得到了国内外专家学者的广泛的研究讨论。盲信号分离技术也因此获得了飞速的发展。然而，这一领域的研究工作还没有达到完全解决问题的程度。这促使我们将盲信号分离算法的研究作为本论文的研究对象。
针对瞬时线性混叠情况下盲信号分离算法中存在的一些问题，对盲信号分离技术的理论、算法进行了较深入的研究。主要工作和创新如下：
(1)：针对FastICA类方法不能保证信号提取的有序或者有目的性以及容易丢失弱信号的问题；提出基于非高斯性极大准则和空间划分的原理，利用智能算法进行优化的盲分离算法。实验也显示：在需要有序提取以及存在微弱信号的情况下，本文算法分离效果优于FastICA算法。
(2)：针对欠定条件下S-ICA算法在源信号不是足够稀疏情况下算法难以达到满意的分离效果的问题，提出在估计混合矩阵的基础上，通过简化混合矩阵建立新的混合矩阵，利用信号的独立性，从观测信号中提取源信号的频谱完成源信号分离的方法。实验结果也说明了算法的有效性。
(3)：研究分析了白化处理对盲信号分离模型中混合矩阵的影响，提出在2源情况下可根据白化数据的峭度和中隐含的信息直接计算分离矩阵的参数的方法。该算法在多源情况下，也只需要少量迭代，且不需考虑迭代初试值对算法的影响。文中实验也证实：该算法可以达到快速有效的完成超高斯和亚高斯的混合信号的分离任务。
(4)：研究了Infomax算法中评价函数的作用以及Ext-Infomax算法中基于峭度的模型切换单一评价函数存在一些不稳定因素。提出根
Blind signal separation(BSS) is an interesting project in the field of signal processing.The technique of BSS can be applied in speech signal process-ing,image processing,communication processing,hydroacoustic signal process-ing,biomedical signal processing,data mining and many others.Because of wide usage of BSS,many researchers have devoted to the research of BSS.and the technique of BBS has been greatly improved.research on BSS has been going on for about twenty years. However,the problem of BSS has not been totally solved.All above stimulate us to be engaged in researches on BSS algorithm.
The main parts of thesis are research on BSS theory and modification to BSS algorithm in difference practical field based on linear mix model.The main work and innovation are abstracted as follows.
Since the algorithm of FastICA can't ensure the extraction of sources in order according to sources's character and fail with weak source,a blind signal extraction algorithm based on intelligent algorithm and Maximization of Non-gaussianity is proposed.AU simulation results show that the proposed algorithm show better performance to above problem than the algorithm of FastICA.
Since S-ICA algorithm requires that sources are very sparse,which leads to bad performance sometimes.A new algorithm is presented by using the characteristic of SPARSE of the signals.It simplifies channel matrix and set up a new one. Based upon the independence among sources, the frequency spec-trums of the sources can be estimated from the observed signals in a new channel model.So that sources can be separated. Simulation studies are available to support the proposed algorithm.
By research white operation how to effect on mix matrix,herein a new simpler and faster method based on higher order statistics is introduced in the 2 sources instance, which can estimate the separation matrix straightly. In more sources instance,only a few iterative operation should be required and there is no need to consider initial value.Good performance of simulations proves the prac-
针对瞬时线性混叠情况下盲信号分离算法中存在的一些问题，对盲信号分离技术的理论、算法进行了较深入的研究。主要工作和创新如下：
(1)：针对FastICA类方法不能保证信号提取的有序或者有目的性以及容易丢失弱信号的问题；提出基于非高斯性极大准则和空间划分的原理，利用智能算法进行优化的盲分离算法。实验也显示：在需要有序提取以及存在微弱信号的情况下，本文算法分离效果优于FastICA算法。
(2)：针对欠定条件下S-ICA算法在源信号不是足够稀疏情况下算法难以达到满意的分离效果的问题，提出在估计混合矩阵的基础上，通过简化混合矩阵建立新的混合矩阵，利用信号的独立性，从观测信号中提取源信号的频谱完成源信号分离的方法。实验结果也说明了算法的有效性。
(3)：研究分析了白化处理对盲信号分离模型中混合矩阵的影响，提出在2源情况下可根据白化数据的峭度和中隐含的信息直接计算分离矩阵的参数的方法。该算法在多源情况下，也只需要少量迭代，且不需考虑迭代初试值对算法的影响。文中实验也证实：该算法可以达到快速有效的完成超高斯和亚高斯的混合信号的分离任务。
(4)：研究了Infomax算法中评价函数的作用以及Ext-Infomax算法中基于峭度的模型切换单一评价函数存在一些不稳定因素。提出根
Blind signal separation(BSS) is an interesting project in the field of signal processing.The technique of BSS can be applied in speech signal process-ing,image processing,communication processing,hydroacoustic signal process-ing,biomedical signal processing,data mining and many others.Because of wide usage of BSS,many researchers have devoted to the research of BSS.and the technique of BBS has been greatly improved.research on BSS has been going on for about twenty years. However,the problem of BSS has not been totally solved.All above stimulate us to be engaged in researches on BSS algorithm.
The main parts of thesis are research on BSS theory and modification to BSS algorithm in difference practical field based on linear mix model.The main work and innovation are abstracted as follows.
Since the algorithm of FastICA can't ensure the extraction of sources in order according to sources's character and fail with weak source,a blind signal extraction algorithm based on intelligent algorithm and Maximization of Non-gaussianity is proposed.AU simulation results show that the proposed algorithm show better performance to above problem than the algorithm of FastICA.
Since S-ICA algorithm requires that sources are very sparse,which leads to bad performance sometimes.A new algorithm is presented by using the characteristic of SPARSE of the signals.It simplifies channel matrix and set up a new one. Based upon the independence among sources, the frequency spec-trums of the sources can be estimated from the observed signals in a new channel model.So that sources can be separated. Simulation studies are available to support the proposed algorithm.
By research white operation how to effect on mix matrix,herein a new simpler and faster method based on higher order statistics is introduced in the 2 sources instance, which can estimate the separation matrix straightly. In more sources instance,only a few iterative operation should be required and there is no need to consider initial value.Good performance of simulations proves the prac-
引文
[1] 刘琚 何振亚．盲源分离和盲反卷积．电子学报，30(4)：570-576，2002．
[2] 张贤达 保铮．盲信号分离．电子学报，29(12)：1766-1771，2001．
[3] 张贤达 朱小军，朱孝龙．盲信号分离研究分类与展望．西安电子科技大学学报(自然科学版)，31(3)：399-404，2004．
[4] J.Herault and C.Jutten. Detection de grandeurs primitives dans un message copmosites par une architecture de calcul neuromimetique en apprentissage non supervise. Nice, Freance, 1985.
[5] J.Herault and C.Jutten. Blind separation of sources,parti:an adaptive algorithm based on neuro mimetic. Signal Processing, 24(1): 1-10, 1991.
[6] J F Cardoso. Blind beamforming for nongaussian signals, lEE Proceedings-F, 140(6):224-230, 1993.
[7] 刘斌 凌燮亭．源于盲分离思想的线性变形图象校正．复旦学报(自然科学版)，34(2)：185-190，1995．
[8] T W Lee, A J Bell, and R Orglmeister. Blind source separation of real world signals. In Proc of ICNN, pages 2129-2134. houston:ICNN, 1997.
[9] S Makeig, T PJung, and A J Bell et al. Blind separation of auditory event related brain responses into independent components, in Proc Natl Acad Sci, 94:10979-10984, 1997.
[10] J Karhunen and A Hyvarinen. Application of neural blind separation to signal and image processing. In Proc of ICNN, pages 131-134. Germany:munich, 1997.
[11] H Sahlin and H Broman. Separation of real world signals. Signal Processing, 64(2):103-113, 1998.
[12] M J Mckeown, T P Jung, and S Mekeig et al. Spatially independent activity patterns in functional mri date during the stroop corlor-naming task. in Proc Natl Acad Sci, 95:803-810, 1998.
[13] 李昕 胡波 凌燮亭 et al．基于盲信号分离的胎儿心电提取．中国生物医学工程学报，21(5)：461-365，2002．
[14] A Cichoki and S. Amari. Adaptive Blind Signal and Image Processing. New York:Wiley, 2002.
[15] A. Hyvarinen. Survey on independent component analysis. Neural Computation, 2(1):96-128, 1999.
[16] Aapo Hyvarinen et.al. Independent Component Analysis. New York:Wiley, 2001.
[17] E. Oja. A simplified neuron model as a principal component analyzer. J. of Mathematical Biology, 15:267-273, 1982.
[18] E. Oja and J. Karhunen. On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix. Journal of Math Analysis and Applications, 106:69-84, 1985.
[19] E. Oja. Neural networks, principal components, and subspaces. Int. J. on Neural Systems, 1:61-68, 1989.
[20] E. Oja, H. Ogawa, and J. Wangviwattana. Learning in nonlinear constrained hebbian networks. In T. Kohonen et al., editor, Artificial Neural Networks, Proc. ICANN'91, volume 8, pages 385-390. Espoo, Finland, 1991.
[21] E. Oja. The nonlinear pea learning rule in independent component analysis. Neuro computing, 17(1):25-46, 1997.
[22] E. Oja. Nonlinear pca criterion and maximum likelihood in independent component analysis. In Proc. Int. Workshop on Independent Component Analysis and Signal Separation (ICA'99), volume 8, pages 143-148. Aussois, France, 1999.
[23] A Cichoki et al. New algorithm for blind separation of sources. Electronics Letters, 28(21): 1986-1987, 1992.
[24] A Cichoki et al. Robust learning algorithm for blind separation of sources. Electronics Letters, 30( 17):1386-1387, 1994.
[25] A Cichoki, R Thawonmas, and S. Amari. Sequential blind extraction in order specified stochastic properties. Electronics Letters, 33(1):64—65, 1997.
[26] Pajunen Petleri and Karhunen J. Least squares methods for blind source separation based on nonlinear pca. Int Journal of Neural Systems, 1998.
[27] V.C. Soon et al L. Tong, R. Liu. Indeterminacy and identifiability of blind identification. IEEE Trans on Circuits and Systems, 38(5):499-509, 1991.
[28] T-W.Lee. Independent Component Analysis-Theory and application. Kluwer, 1998.
[29] M. Girolami, editor. Advances in Independent Component Analysis. Springer-Verlag, 2000.
[30] K E Hild II, D Erdogmus, and J C Principe. Blind source separation of time-varying instantaneous mixtures using an on-line algorithm. In Proc. IEEE Intl. Conf. on Acoustic, Speech and Signal Pwc.,ICASSP'02, volume 5, pages 993-996, 2002.
[31] K E Hild II, D Erdogmus, and J C Principe. On-line minimum mutual information method for time-varying blind source separation. In IEEE Intl. Conf. on Acoustic, Speech and Signal Proc.,ICASSP'01[C], 2001.
[32] A Yeredor. Tv-sobi:an expansion of sobi for linearly time-varying mixtures. In Proc. IEEE Intl. Conf. on Acoustic, Speech and Signal Proc. ,ICASSP '03, volume 5, pages 903-908,2003.
[33] Pierre Comon. Independent component analysis,a new concept? Signal Processing, 36(3):287-314, 1994.
[34] Liu R W Cao X R. General approach to blind signal separation. IEEE Tranc. On Signal Processing, 44(3):562-571, 1996.
[35] J F Cardoso. blind siganl separation:statistical principles. proc IEEE, 86(10):2009-2025, 1997.
[36] T W Lee, M Girolami, and A J Bell et al. A unifying information theoretic framework for independent component analysis. Computers and Mathmatics with Applications, 31 (11): 1 -21, 2000.
[37] T. D. Sanger. Optimal unsupervised learning in a single layer linear feedforward neural network. Neural Network, 2:459-473, 1989.
[38] J Karhunen and E Oja P Pajunnen P. The nonlinear pca criterion in blind separation: Relation whith other approaches. Neural Computing, 22(1):5-20, 1998.
[39] J P Nadal and N Parga. Non linear neurons in the low noiselimit:a factorial code maximizes information transfer. Network, 4:295-312, 1994.
[40] E. Oja. Blind source separation:neural net principles and applications. In Proc. of SPIE, volume 5439, pages 1-17. Bellingham, WA, 2004.
[41] A. Hyvarinen and E. Oja. A fast fixed-point algorithm for independent component analysis. Neural Computation, 9(7): 1483-1492, 1997.
[42] A Hyvarinen. A family of fixed-point algorithm for independent component analysis. In Proc. ICASSP, pages 3917-3920, 1997.
[43] A. Hyvarinen. Fast and robust fixed-point algorithms for independent component analysis. IEEE Trans. on Neural Networks, 10(3):626-634, 1999.
[44] Simon Haykin. Adaptive Filter Theol. (Third Edition).
[45] 易大义 陈道琦．数值分析引论．浙江大学出版社，1998．
[46] Hyun-Kyo Jang Jang-Sung Chun, Min-Kyu Kim. Shape optimization of electromagnetic devices using immune algorithm. IEEE Trans. On Magnetics, 48(2): 1876-1879, 1997.
[47] Holland J H. Adaptation in Nature and Artifical Systems. The University of Michigan Press, Ann Arbor, 1975.
[48] S. Amari and A. Cichocki. A new learning algorithm for blind source separation. In Advances in Neural Information Processing, volume 8, pages 657-663. MIT Press, Cambridge, MA, 1996.
[49] D Obradovic and G Deco. Information maximization and independent component analysis:is there a difference? Neural Computation, 10(8):2085-2101, 1998.
[50] R.Linsker. Self-organization in a perceptual network. Computer, 21:105-117, 1988.
[51] 凌燮亭．延时狭带信号的自学习盲分离．电子学报，23(1)：28-33，1995．
[52] 凌燮亭．近场宽带信号源的盲分离．电子学报，24(7)：87-91，1996．
[53] 赵青 俞承芳 凌燮亭．前馈神经网络盲信号分离的实验研究．复旦学报(自然科学版)，36(3)：344-348，1997．
[54] A J Bell and T J Sejnowski. An information-maximization approach to blind separation and blind deconvolution. Neural Computation, 7:1129-1159, 1995.
[55] J F Cardoso. Infomax and maximum likelihood for blind source separation. IEEE Signal Processing Letters, 4(4): 112-114, 1997.
[56] Lacoume J Gaeta M. Source separation without a priori knowledge: The maximum liklihood solution. Signal Processing V: Theories and Application, pages 621-624, 1990.
[57] Fyfe C Girolami M. Negentropy and kurtosis as projection pursuit indices provide generalised ica algorithms. NIPS96 Blind Signal Separation Workshop, pages 621-624, 1996.
[58] 章晋龙 谢胜利．基于qr分解的最大负熵盲分离算法．通讯学报，25(4)：75-83，2004．
[59] S Y Kung and C Mejuto. Extraction of independent components from hybrid mixture:kuicnet learning algorithm and aplication. In Proc of ICASSP'98, pages 1209-1212, 2 1998.
[60] Ohnishi N et al Mansour A. Blind multiuser separation of instantaneous mixture algorithm based on geometrical concept. Signal Processing, 82(2):1155-1175, 2002.
[61] 章晋龙 谢胜利．基于旋转变换的最小互信息量盲分离算法．电子学报，30(5)：628-631，2002．
[62] 章晋龙 谢胜利，何昭水．基于遗传算法的有序盲信号提取．电子学报，32(4)：616-619，2004．
[63] 汪军 何振亚．瞬时混叠信号盲分离．电子学报，25(4)：1-4，1997．
[64] 刘琚 何振业．利用高阶累积量和独立分量分析网络进行盲均衡与系统辨识．数据采集与处理，13(3)：201-205，1998．
[65] 何振亚 刘琚．基于累积量展开的神经网络盲源分离方法．通信学报，20：76-82，1999．
[66] 何振亚 杨绿溪 鲁子奕．非线性infomax自组织算法的盲源分离机理．数据采集与处理，13(4)：303-305，1998．
[67] 杨绿溪 何振亚 鲁子奕．线性infomax自组织算法的性能分析．数据采集与处理，13(4)：306-310，1998．
[68] He Zheng Ya, Liu JU, and Yang LuXi. Blind separation of mages using edge worth expansion based ica algorithm. Chinese Journal of Electronics, 8(3):278-282, 1999.
[69] He Zheng Ya, Yang LuXi, and Liu JU. Blind source separation using cluster based multivariate density estimation algorithm. IEEE Trans on Signal Processing, 48(2):575-579, 2000.
[70] 刘琚 何振亚．线性混迭信号中独立源的盲提取．应用科学学报，19(3)：210-213．2001．
[71] 汪军 何振亚．卷积混叠信号盲分离．电子学报，25(7)：7-11，1997．
[72] B A Pearlmutter and L C Parra. A context sensitive geralization of ica. In Proc of ICONIP, pages 151-157. Hong Kong:ICONIP, 1996.
[73] J joutsensalo T Ristaniemi. Advanced ica-based receivers for dscdma systems. In Proc 11th IEEE International symposium on Personal ,indoor ,and Mobile Radio communication, pages 276-281. London, Sep 2000.
[74] Maite Brandt-Pearce. Signal separation using fractional sampling in multiuser communications. IEEE Tranc. On COMMUNICATIONS, 48(2):242-251, 2000.
[75] 何振亚 陈宇欣．一种基于特征空间的肓波束形成算法．数据采集与处理，14(3)：263-266，1999．
[76] 何振亚 陈宇欣．用hopfield网络实现盲波束形成．通信学报，20(12)：86-91，1999．
[77] 何振亚 陈宇欣．一种归一化快速盲自适应波束形成算法．应用科学学报，17(2)：163-168，1999．
[78] 何振亚 陈宇欣．一种基于周期平稳信号特性的递归盲波束形成算法．电子科技大学学报，29(3)：243-246，2000．
[79] V Zarzoso and A K Nandi. Adaptive blind source separation for virtually any source probability density function. IEEE Trans Signal Processing, 48(2):477-488, 2000.
[80] Douglas S.C. Mathis H. On the existence of universal nonlinearities for blind source separation. IEEE Trans on Signal Processing, 50(5): 1007-1016, 2002.
[81] et al. cardo Boscolo, Hong Pan. Independent component analysis based on non- parametric density estimation. IEEE Transactions On NEURAL NETWORKS, 15(1):55-65, 2004.
[82] Sejnowski T J Lee T W, Girolami M. Independent component analysis using an extended infomax algorithm for mixed sub-gaussian and guassian sources. Neural Computation, pages 609-633, 1998.
[83] 杨绿溪 李克 周长春何振业．一种用于超高斯于业高斯混合信号盲分离的新方法．东南大学学报，29(1)，1999．
[84] 胡光锐 虞晓．基于高斯混合密度函数估计的语音分离．上海交通大学学报，34(2)：177-180，2000．
[85] 史见智 张洪渊．一种用于超高斯和亚高斯混合信号盲分离的新算法．电子学报，29(10)：1392-1396，2001．
[86] 陈阳 何振亚 杨绿溪．数格子——一种简单的盲源分离方法．数据采集与处理，17(1)：5-9，2002．
[87] G J Scruby and S J Flockton. On-line tracking for blind source separation using zero-point probability, IEE Savoy Place London WC2R OBL, UK, 1997.
[88] M Enescu and Koivunen. Tracking time-varying mixing system in blind separation. Sensor Array and Multichannel Signal Processing Workshop, 3:291-295, 2000.
[89] K E Hild Ⅱ and D Erdogmus et al. Blind source separation using renyi's mutual information. IEEE Signal Pro. Letters, 8(6):174-176, June 2001.
[90] Ryo Mukai et al. Robust real-time blind source separation for moving speakers in a room. In Proc. IEEE Intl. Conf on Acoustic, Speech and Signal Proc.,ICASSP'03, volume 5, pages 469-472, 2003.
[91] A Yeredor. Time-delay estimation in mixtures. In Proc. IEEE Intl. Conf on Acoustic, Speech and Signal Proc.,ICASSP'03, volume 5, pages 237-240, 2003.
[92] A Belouchrani and K A meraim et al. A blind source separation technique using second-order stastistics. IEEE Trans Signal Processing, 15(2):434-444, 1997.
[93] Barak A Pearlmutter and Vamsi K Potluru. Sparse separation: Principles and tricks. Proceedings of SPIE, 5102, 2003.
[94] Shoko Araki and Shoji Makino. Underdetermined blind separation for speech in real environments with sparseness and ica. In Proc ICASSP2004, pages 881-884, 2004.
[95] B. Emile, P. Comon, and J. Le Roux. Estimation of time delays with fewer sensors than sources. IEEE Transactions on Signal Processing, 46(7):2012-2015, July 1998.
[96] Pierre Comon. Blind identification and source separation in 2×3 under- determined mixtures. IEEE Transaction on Signal Processing, 52, Jan 2004.
[97] Andrzej Cichocki Juha Karvanenl. Measuring sparseness of noisy signal. In Proc 4th ICA2003, pages 125-151. Japan,Nara, Apr 2003.
[98] P Bofill and M Zibulevsky. Blind separation of more sources than mixtures using sparsity of their short-time fourier transform. In International Workshop on Independent Component Analysis and Blind Signal Separation, pages 87-92. Helsinki, Finland, June 1999.
[99] M Zibulevsky and B A Pearlmutter. Blind source separation by sparse decomposition in a signal dictionary. Neural Computation, 13(4):863-882, 2001.
[100] M Van Hulle. Clustering approach to square and non-square blind source separation. In IEEE Workshop on Neural Networks for Signal Processing (NNSP99), pages 315-323, Aug 1999.
[101] Te-Won Lee and M.S. Lewicki. Blind source separation of more sources than mixtures using overcomplete representations. IEEE Transactions on Signal Processing, 41 (12):3397-3415, 1999.
[102] S Hochreiter and M C Mozer. Monaural separation and classification of mixed signals:a support-vector regression perspective. In 3rd International Conference on Independent Component Analysis and Blind Signal Separation. San Diego, CA, 2001.
[103] S Rickard, J Balan, and J Rosca. Doa estimation of many w-disjoint orthogonal source from two mixture using duet. In Proceedings of the 10th IEEE Workshop on Stastical Signal and Array Processing(SSAP2000), pages 311-314. Pocono Manor, PA, 2000.
[104] Alexander Jourjine, S Rickard, and Ozaur Yilmaz. Blind separation of disjoint orthogonal signal:demixing n source form 2 mixtures mixture. In Proc ICASSP2000, volume 5, pages 2985-2988. Istanbul, Turkey, June 2000.
[105] S Rickard, J Balan, and J Rosca. Real-time time-frequency based blind source separation. In 3rd International Conference on Independent Component Analysis and Blind Source Separation. San Diego, CA, Dec 2001.
[106] S Rickard and Ozaur Yilmaz. On the approximate w-disjoint orthogonality of speech. In Proc ICASSP2002. Orlando Florida, USA,. May 2002.
[107] 徐尚志 徐旭 叶中付．基于遗传算法的doa估计．中国科学技术大学学报，34(3)：361-365，2004．
[108] 叶中付 沈凤麟．Doa估计中自相关矩阵的时空二维估计方法．信号处理，11(3)：206-212，1995．
[109] 叶中付 徐旭 吴涛．一种新的基于多用户去相关的波达方向估计方法．中国科学技术大学学报，34(2)：183-189，2004．
[110] 叶中付．一种基于四阶累量的二维空间谱估计的方法．通信学报，18(3)：51-54．1998．
[111] Pando Georgiev, Fabian Theis, and Andrzej Cichocki. Blind source separation and sparse component analysis of overcomplete mixtures. In Proc ICASSP2004, pages 493-496, 2004.
[112] 沈凤麟 叶中付 钱玉美．信号统计分析与处理．中国科学技术大学出版社，合肥，2001．
[113] 张贤达．现代信号处理．清华大学出版社，北京，1995．
[114] 胡广书．数字信号处理．理论、算法与实现．清华大学出版社，北京，8 1997．
[115] 姜丹．信息论与编码．中国科学技术大学出版社，合肥，2001．
[116] S.-I. Amari. Natural gradient works efficiently in learning. Neural Computation, 10(2):251-276, 1998.
[117] P Bofill and M Zibulevsky. Underdetermined blind source separation using sparse representations. Signal Processing, 81 (11):2353-2362, 2001.
[118] Kai Yu and Boling Xu. Suppressing cocktail party noise for speech acquisition. Signal Processing Proceedings, WCCC-ICSP 2000.5th International Conference on, 2:21-25, Aug 2000.
[2] 张贤达 保铮．盲信号分离．电子学报，29(12)：1766-1771，2001．
[3] 张贤达 朱小军，朱孝龙．盲信号分离研究分类与展望．西安电子科技大学学报(自然科学版)，31(3)：399-404，2004．
[4] J.Herault and C.Jutten. Detection de grandeurs primitives dans un message copmosites par une architecture de calcul neuromimetique en apprentissage non supervise. Nice, Freance, 1985.
[5] J.Herault and C.Jutten. Blind separation of sources,parti:an adaptive algorithm based on neuro mimetic. Signal Processing, 24(1): 1-10, 1991.
[6] J F Cardoso. Blind beamforming for nongaussian signals, lEE Proceedings-F, 140(6):224-230, 1993.
[7] 刘斌 凌燮亭．源于盲分离思想的线性变形图象校正．复旦学报(自然科学版)，34(2)：185-190，1995．
[8] T W Lee, A J Bell, and R Orglmeister. Blind source separation of real world signals. In Proc of ICNN, pages 2129-2134. houston:ICNN, 1997.
[9] S Makeig, T PJung, and A J Bell et al. Blind separation of auditory event related brain responses into independent components, in Proc Natl Acad Sci, 94:10979-10984, 1997.
[10] J Karhunen and A Hyvarinen. Application of neural blind separation to signal and image processing. In Proc of ICNN, pages 131-134. Germany:munich, 1997.
[11] H Sahlin and H Broman. Separation of real world signals. Signal Processing, 64(2):103-113, 1998.
[12] M J Mckeown, T P Jung, and S Mekeig et al. Spatially independent activity patterns in functional mri date during the stroop corlor-naming task. in Proc Natl Acad Sci, 95:803-810, 1998.
[13] 李昕 胡波 凌燮亭 et al．基于盲信号分离的胎儿心电提取．中国生物医学工程学报，21(5)：461-365，2002．
[14] A Cichoki and S. Amari. Adaptive Blind Signal and Image Processing. New York:Wiley, 2002.
[15] A. Hyvarinen. Survey on independent component analysis. Neural Computation, 2(1):96-128, 1999.
[16] Aapo Hyvarinen et.al. Independent Component Analysis. New York:Wiley, 2001.
[17] E. Oja. A simplified neuron model as a principal component analyzer. J. of Mathematical Biology, 15:267-273, 1982.
[18] E. Oja and J. Karhunen. On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix. Journal of Math Analysis and Applications, 106:69-84, 1985.
[19] E. Oja. Neural networks, principal components, and subspaces. Int. J. on Neural Systems, 1:61-68, 1989.
[20] E. Oja, H. Ogawa, and J. Wangviwattana. Learning in nonlinear constrained hebbian networks. In T. Kohonen et al., editor, Artificial Neural Networks, Proc. ICANN'91, volume 8, pages 385-390. Espoo, Finland, 1991.
[21] E. Oja. The nonlinear pea learning rule in independent component analysis. Neuro computing, 17(1):25-46, 1997.
[22] E. Oja. Nonlinear pca criterion and maximum likelihood in independent component analysis. In Proc. Int. Workshop on Independent Component Analysis and Signal Separation (ICA'99), volume 8, pages 143-148. Aussois, France, 1999.
[23] A Cichoki et al. New algorithm for blind separation of sources. Electronics Letters, 28(21): 1986-1987, 1992.
[24] A Cichoki et al. Robust learning algorithm for blind separation of sources. Electronics Letters, 30( 17):1386-1387, 1994.
[25] A Cichoki, R Thawonmas, and S. Amari. Sequential blind extraction in order specified stochastic properties. Electronics Letters, 33(1):64—65, 1997.
[26] Pajunen Petleri and Karhunen J. Least squares methods for blind source separation based on nonlinear pca. Int Journal of Neural Systems, 1998.
[27] V.C. Soon et al L. Tong, R. Liu. Indeterminacy and identifiability of blind identification. IEEE Trans on Circuits and Systems, 38(5):499-509, 1991.
[28] T-W.Lee. Independent Component Analysis-Theory and application. Kluwer, 1998.
[29] M. Girolami, editor. Advances in Independent Component Analysis. Springer-Verlag, 2000.
[30] K E Hild II, D Erdogmus, and J C Principe. Blind source separation of time-varying instantaneous mixtures using an on-line algorithm. In Proc. IEEE Intl. Conf. on Acoustic, Speech and Signal Pwc.,ICASSP'02, volume 5, pages 993-996, 2002.
[31] K E Hild II, D Erdogmus, and J C Principe. On-line minimum mutual information method for time-varying blind source separation. In IEEE Intl. Conf. on Acoustic, Speech and Signal Proc.,ICASSP'01[C], 2001.
[32] A Yeredor. Tv-sobi:an expansion of sobi for linearly time-varying mixtures. In Proc. IEEE Intl. Conf. on Acoustic, Speech and Signal Proc. ,ICASSP '03, volume 5, pages 903-908,2003.
[33] Pierre Comon. Independent component analysis,a new concept? Signal Processing, 36(3):287-314, 1994.
[34] Liu R W Cao X R. General approach to blind signal separation. IEEE Tranc. On Signal Processing, 44(3):562-571, 1996.
[35] J F Cardoso. blind siganl separation:statistical principles. proc IEEE, 86(10):2009-2025, 1997.
[36] T W Lee, M Girolami, and A J Bell et al. A unifying information theoretic framework for independent component analysis. Computers and Mathmatics with Applications, 31 (11): 1 -21, 2000.
[37] T. D. Sanger. Optimal unsupervised learning in a single layer linear feedforward neural network. Neural Network, 2:459-473, 1989.
[38] J Karhunen and E Oja P Pajunnen P. The nonlinear pca criterion in blind separation: Relation whith other approaches. Neural Computing, 22(1):5-20, 1998.
[39] J P Nadal and N Parga. Non linear neurons in the low noiselimit:a factorial code maximizes information transfer. Network, 4:295-312, 1994.
[40] E. Oja. Blind source separation:neural net principles and applications. In Proc. of SPIE, volume 5439, pages 1-17. Bellingham, WA, 2004.
[41] A. Hyvarinen and E. Oja. A fast fixed-point algorithm for independent component analysis. Neural Computation, 9(7): 1483-1492, 1997.
[42] A Hyvarinen. A family of fixed-point algorithm for independent component analysis. In Proc. ICASSP, pages 3917-3920, 1997.
[43] A. Hyvarinen. Fast and robust fixed-point algorithms for independent component analysis. IEEE Trans. on Neural Networks, 10(3):626-634, 1999.
[44] Simon Haykin. Adaptive Filter Theol. (Third Edition).
[45] 易大义 陈道琦．数值分析引论．浙江大学出版社，1998．
[46] Hyun-Kyo Jang Jang-Sung Chun, Min-Kyu Kim. Shape optimization of electromagnetic devices using immune algorithm. IEEE Trans. On Magnetics, 48(2): 1876-1879, 1997.
[47] Holland J H. Adaptation in Nature and Artifical Systems. The University of Michigan Press, Ann Arbor, 1975.
[48] S. Amari and A. Cichocki. A new learning algorithm for blind source separation. In Advances in Neural Information Processing, volume 8, pages 657-663. MIT Press, Cambridge, MA, 1996.
[49] D Obradovic and G Deco. Information maximization and independent component analysis:is there a difference? Neural Computation, 10(8):2085-2101, 1998.
[50] R.Linsker. Self-organization in a perceptual network. Computer, 21:105-117, 1988.
[51] 凌燮亭．延时狭带信号的自学习盲分离．电子学报，23(1)：28-33，1995．
[52] 凌燮亭．近场宽带信号源的盲分离．电子学报，24(7)：87-91，1996．
[53] 赵青 俞承芳 凌燮亭．前馈神经网络盲信号分离的实验研究．复旦学报(自然科学版)，36(3)：344-348，1997．
[54] A J Bell and T J Sejnowski. An information-maximization approach to blind separation and blind deconvolution. Neural Computation, 7:1129-1159, 1995.
[55] J F Cardoso. Infomax and maximum likelihood for blind source separation. IEEE Signal Processing Letters, 4(4): 112-114, 1997.
[56] Lacoume J Gaeta M. Source separation without a priori knowledge: The maximum liklihood solution. Signal Processing V: Theories and Application, pages 621-624, 1990.
[57] Fyfe C Girolami M. Negentropy and kurtosis as projection pursuit indices provide generalised ica algorithms. NIPS96 Blind Signal Separation Workshop, pages 621-624, 1996.
[58] 章晋龙 谢胜利．基于qr分解的最大负熵盲分离算法．通讯学报，25(4)：75-83，2004．
[59] S Y Kung and C Mejuto. Extraction of independent components from hybrid mixture:kuicnet learning algorithm and aplication. In Proc of ICASSP'98, pages 1209-1212, 2 1998.
[60] Ohnishi N et al Mansour A. Blind multiuser separation of instantaneous mixture algorithm based on geometrical concept. Signal Processing, 82(2):1155-1175, 2002.
[61] 章晋龙 谢胜利．基于旋转变换的最小互信息量盲分离算法．电子学报，30(5)：628-631，2002．
[62] 章晋龙 谢胜利，何昭水．基于遗传算法的有序盲信号提取．电子学报，32(4)：616-619，2004．
[63] 汪军 何振亚．瞬时混叠信号盲分离．电子学报，25(4)：1-4，1997．
[64] 刘琚 何振业．利用高阶累积量和独立分量分析网络进行盲均衡与系统辨识．数据采集与处理，13(3)：201-205，1998．
[65] 何振亚 刘琚．基于累积量展开的神经网络盲源分离方法．通信学报，20：76-82，1999．
[66] 何振亚 杨绿溪 鲁子奕．非线性infomax自组织算法的盲源分离机理．数据采集与处理，13(4)：303-305，1998．
[67] 杨绿溪 何振亚 鲁子奕．线性infomax自组织算法的性能分析．数据采集与处理，13(4)：306-310，1998．
[68] He Zheng Ya, Liu JU, and Yang LuXi. Blind separation of mages using edge worth expansion based ica algorithm. Chinese Journal of Electronics, 8(3):278-282, 1999.
[69] He Zheng Ya, Yang LuXi, and Liu JU. Blind source separation using cluster based multivariate density estimation algorithm. IEEE Trans on Signal Processing, 48(2):575-579, 2000.
[70] 刘琚 何振亚．线性混迭信号中独立源的盲提取．应用科学学报，19(3)：210-213．2001．
[71] 汪军 何振亚．卷积混叠信号盲分离．电子学报，25(7)：7-11，1997．
[72] B A Pearlmutter and L C Parra. A context sensitive geralization of ica. In Proc of ICONIP, pages 151-157. Hong Kong:ICONIP, 1996.
[73] J joutsensalo T Ristaniemi. Advanced ica-based receivers for dscdma systems. In Proc 11th IEEE International symposium on Personal ,indoor ,and Mobile Radio communication, pages 276-281. London, Sep 2000.
[74] Maite Brandt-Pearce. Signal separation using fractional sampling in multiuser communications. IEEE Tranc. On COMMUNICATIONS, 48(2):242-251, 2000.
[75] 何振亚 陈宇欣．一种基于特征空间的肓波束形成算法．数据采集与处理，14(3)：263-266，1999．
[76] 何振亚 陈宇欣．用hopfield网络实现盲波束形成．通信学报，20(12)：86-91，1999．
[77] 何振亚 陈宇欣．一种归一化快速盲自适应波束形成算法．应用科学学报，17(2)：163-168，1999．
[78] 何振亚 陈宇欣．一种基于周期平稳信号特性的递归盲波束形成算法．电子科技大学学报，29(3)：243-246，2000．
[79] V Zarzoso and A K Nandi. Adaptive blind source separation for virtually any source probability density function. IEEE Trans Signal Processing, 48(2):477-488, 2000.
[80] Douglas S.C. Mathis H. On the existence of universal nonlinearities for blind source separation. IEEE Trans on Signal Processing, 50(5): 1007-1016, 2002.
[81] et al. cardo Boscolo, Hong Pan. Independent component analysis based on non- parametric density estimation. IEEE Transactions On NEURAL NETWORKS, 15(1):55-65, 2004.
[82] Sejnowski T J Lee T W, Girolami M. Independent component analysis using an extended infomax algorithm for mixed sub-gaussian and guassian sources. Neural Computation, pages 609-633, 1998.
[83] 杨绿溪 李克 周长春何振业．一种用于超高斯于业高斯混合信号盲分离的新方法．东南大学学报，29(1)，1999．
[84] 胡光锐 虞晓．基于高斯混合密度函数估计的语音分离．上海交通大学学报，34(2)：177-180，2000．
[85] 史见智 张洪渊．一种用于超高斯和亚高斯混合信号盲分离的新算法．电子学报，29(10)：1392-1396，2001．
[86] 陈阳 何振亚 杨绿溪．数格子——一种简单的盲源分离方法．数据采集与处理，17(1)：5-9，2002．
[87] G J Scruby and S J Flockton. On-line tracking for blind source separation using zero-point probability, IEE Savoy Place London WC2R OBL, UK, 1997.
[88] M Enescu and Koivunen. Tracking time-varying mixing system in blind separation. Sensor Array and Multichannel Signal Processing Workshop, 3:291-295, 2000.
[89] K E Hild Ⅱ and D Erdogmus et al. Blind source separation using renyi's mutual information. IEEE Signal Pro. Letters, 8(6):174-176, June 2001.
[90] Ryo Mukai et al. Robust real-time blind source separation for moving speakers in a room. In Proc. IEEE Intl. Conf on Acoustic, Speech and Signal Proc.,ICASSP'03, volume 5, pages 469-472, 2003.
[91] A Yeredor. Time-delay estimation in mixtures. In Proc. IEEE Intl. Conf on Acoustic, Speech and Signal Proc.,ICASSP'03, volume 5, pages 237-240, 2003.
[92] A Belouchrani and K A meraim et al. A blind source separation technique using second-order stastistics. IEEE Trans Signal Processing, 15(2):434-444, 1997.
[93] Barak A Pearlmutter and Vamsi K Potluru. Sparse separation: Principles and tricks. Proceedings of SPIE, 5102, 2003.
[94] Shoko Araki and Shoji Makino. Underdetermined blind separation for speech in real environments with sparseness and ica. In Proc ICASSP2004, pages 881-884, 2004.
[95] B. Emile, P. Comon, and J. Le Roux. Estimation of time delays with fewer sensors than sources. IEEE Transactions on Signal Processing, 46(7):2012-2015, July 1998.
[96] Pierre Comon. Blind identification and source separation in 2×3 under- determined mixtures. IEEE Transaction on Signal Processing, 52, Jan 2004.
[97] Andrzej Cichocki Juha Karvanenl. Measuring sparseness of noisy signal. In Proc 4th ICA2003, pages 125-151. Japan,Nara, Apr 2003.
[98] P Bofill and M Zibulevsky. Blind separation of more sources than mixtures using sparsity of their short-time fourier transform. In International Workshop on Independent Component Analysis and Blind Signal Separation, pages 87-92. Helsinki, Finland, June 1999.
[99] M Zibulevsky and B A Pearlmutter. Blind source separation by sparse decomposition in a signal dictionary. Neural Computation, 13(4):863-882, 2001.
[100] M Van Hulle. Clustering approach to square and non-square blind source separation. In IEEE Workshop on Neural Networks for Signal Processing (NNSP99), pages 315-323, Aug 1999.
[101] Te-Won Lee and M.S. Lewicki. Blind source separation of more sources than mixtures using overcomplete representations. IEEE Transactions on Signal Processing, 41 (12):3397-3415, 1999.
[102] S Hochreiter and M C Mozer. Monaural separation and classification of mixed signals:a support-vector regression perspective. In 3rd International Conference on Independent Component Analysis and Blind Signal Separation. San Diego, CA, 2001.
[103] S Rickard, J Balan, and J Rosca. Doa estimation of many w-disjoint orthogonal source from two mixture using duet. In Proceedings of the 10th IEEE Workshop on Stastical Signal and Array Processing(SSAP2000), pages 311-314. Pocono Manor, PA, 2000.
[104] Alexander Jourjine, S Rickard, and Ozaur Yilmaz. Blind separation of disjoint orthogonal signal:demixing n source form 2 mixtures mixture. In Proc ICASSP2000, volume 5, pages 2985-2988. Istanbul, Turkey, June 2000.
[105] S Rickard, J Balan, and J Rosca. Real-time time-frequency based blind source separation. In 3rd International Conference on Independent Component Analysis and Blind Source Separation. San Diego, CA, Dec 2001.
[106] S Rickard and Ozaur Yilmaz. On the approximate w-disjoint orthogonality of speech. In Proc ICASSP2002. Orlando Florida, USA,. May 2002.
[107] 徐尚志 徐旭 叶中付．基于遗传算法的doa估计．中国科学技术大学学报，34(3)：361-365，2004．
[108] 叶中付 沈凤麟．Doa估计中自相关矩阵的时空二维估计方法．信号处理，11(3)：206-212，1995．
[109] 叶中付 徐旭 吴涛．一种新的基于多用户去相关的波达方向估计方法．中国科学技术大学学报，34(2)：183-189，2004．
[110] 叶中付．一种基于四阶累量的二维空间谱估计的方法．通信学报，18(3)：51-54．1998．
[111] Pando Georgiev, Fabian Theis, and Andrzej Cichocki. Blind source separation and sparse component analysis of overcomplete mixtures. In Proc ICASSP2004, pages 493-496, 2004.
[112] 沈凤麟 叶中付 钱玉美．信号统计分析与处理．中国科学技术大学出版社，合肥，2001．
[113] 张贤达．现代信号处理．清华大学出版社，北京，1995．
[114] 胡广书．数字信号处理．理论、算法与实现．清华大学出版社，北京，8 1997．
[115] 姜丹．信息论与编码．中国科学技术大学出版社，合肥，2001．
[116] S.-I. Amari. Natural gradient works efficiently in learning. Neural Computation, 10(2):251-276, 1998.
[117] P Bofill and M Zibulevsky. Underdetermined blind source separation using sparse representations. Signal Processing, 81 (11):2353-2362, 2001.
[118] Kai Yu and Boling Xu. Suppressing cocktail party noise for speech acquisition. Signal Processing Proceedings, WCCC-ICSP 2000.5th International Conference on, 2:21-25, Aug 2000.