基于独立分量分析的盲分离算法研究
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摘要
盲信号分离(Blind Source Separation, BSS)是在混合过程未知(即所谓“盲”)的情况下,从观察到的统计独立的源信号的混合数据中恢复一系列源信号的信号分离过程。研究含噪模型的信号盲分离问题具有广泛的应用前景。本文主要讨论了在盲源分离中最常见的源信号线性瞬时混合模型的盲分离问题,同时研究了解决该问题的独立分量分析技术,通过研究与实验,提出了一种新的盲分离算法,该算法能有效实现叠加高斯噪声的混合信号盲分离。
文章首先阐述了信号盲分离问题的基本理论——统计理论和信息论的一些知识;介绍了盲信号分离的基本思想——独立分量分析(ICA),研究对比了一些经典盲分离算法的原理和特点;介绍了盲分离算法的性能评价准则。
盲源分离算法通常需预先假设源信号的概率密度函数,并由此获得关键的核函数,进而从混合信号中分离出源信号。但若假设的概率密度函数与真实概率密度函数差异较大,源信号将不能被正确分离。一般由假设的概率密度函数得到的核函数只能分离出单独的超高斯信号或亚高斯信号。针对此问题,本文以信息论为基础,基于信息极大化和自然梯度原理,运用了一种超高斯与亚高斯混合信号的盲分离方法。该方法联合利用高斯函数与双曲正割函数平方的乘积和两个高斯函数的组合对源信号概率密度函数进行估计,采用峰度信息作为参数来选择概率密度模型及相应的非线性函数;但是此方法因为存在白化约束条件,因而对一些非平稳信号存在不稳定性,为了消除这种白化约束算法对一些非平稳信号的不稳定性,放宽了白化约束条件(称为不完整约束)。
在含有噪声的情况下,一般的盲分离算法不会取得很好的效果,本文用小波变换与上述方法相结合对含有高斯噪声的混合信号进行分离,首先对混合信号进行去噪声处理,但是进行消噪时不能太彻底,以尽可能不损坏观测信号中的有用成分,然而这样带来的问题就是分离信号中会存在明显的噪声残留,针对这一情况,我们再次利用小波变换对分离后的信号进行再消噪,从而得到更好的分离信号,实现了含有噪声的超高斯与亚高斯混合信号的盲分离,通过实验仿真证明了算法的有效性。
Blind signal separation (BSS) is a separation process that extract a series of signal source from the mixed data on the mixing process is unknown (the so-called "blind") .The noise model study with blind signal separation issue has broad application prospects. In this paper, we propose an approach to blind source separation of linear mixtures of the signals that the observations are contaminated with Gaussian noise.
Firstly, we introduce the basic theory of independent component analysis, high order theory and the information theory, analyses the principle and characteristic of some classical algorithms.
Blind source separation algorithm usually assume that the source signals in the prior probability density function, and thus access to critical nuclear function, and then isolated from the mixed-signal source signal. However, the assumption that the probability density function and a real probability density function different, the source will not be the correct signal separation. By the general assumption that the probability density function of the kernel function can be isolated from separate sub-Gaussian signal or super-signals. To solve this problem, this paper based on information theory, based on information of great principle and natural gradient, a super-Gaussian and mixed-signal-Blind separation method. The method combined use of Gaussian function and hyperbolic secant square function and the product of the combination of two Gaussian function of the signal source to estimate the probability density function, the peak of the information used as a parameter to choose probability density and the nonlinear model Function. But this method because of the white constraint conditions, so the number of non-stationary signals exist Stability, in order to eliminate this albino and bound algorithm to a number of non-stationary signals is unstable, and the albino relax restrictive conditions (known as incomplete constraints).
In the presence of noise, the general blind separation algorithm will not get good results, in this paper, the wavelet transform and the method of combining containing Gaussian noise mixed-signal separation. First of mixed signals to deal with noise, but when a eliminate noising can not be too thorough, to the extent possible, does not damage a useful observation signal components, but the problem is that this separation signal there will be significant residual noise. In view of this situation, we are once again using the wavelet transform the separation signal to noise elimination, and thus be better signal separation, the method effectively realize the contained noise of the super-Gaussian and mixed-signal Blind Separation, through simulation proved the effectiveness of the algorithm.
文章首先阐述了信号盲分离问题的基本理论——统计理论和信息论的一些知识;介绍了盲信号分离的基本思想——独立分量分析(ICA),研究对比了一些经典盲分离算法的原理和特点;介绍了盲分离算法的性能评价准则。
盲源分离算法通常需预先假设源信号的概率密度函数,并由此获得关键的核函数,进而从混合信号中分离出源信号。但若假设的概率密度函数与真实概率密度函数差异较大,源信号将不能被正确分离。一般由假设的概率密度函数得到的核函数只能分离出单独的超高斯信号或亚高斯信号。针对此问题,本文以信息论为基础,基于信息极大化和自然梯度原理,运用了一种超高斯与亚高斯混合信号的盲分离方法。该方法联合利用高斯函数与双曲正割函数平方的乘积和两个高斯函数的组合对源信号概率密度函数进行估计,采用峰度信息作为参数来选择概率密度模型及相应的非线性函数;但是此方法因为存在白化约束条件,因而对一些非平稳信号存在不稳定性,为了消除这种白化约束算法对一些非平稳信号的不稳定性,放宽了白化约束条件(称为不完整约束)。
在含有噪声的情况下,一般的盲分离算法不会取得很好的效果,本文用小波变换与上述方法相结合对含有高斯噪声的混合信号进行分离,首先对混合信号进行去噪声处理,但是进行消噪时不能太彻底,以尽可能不损坏观测信号中的有用成分,然而这样带来的问题就是分离信号中会存在明显的噪声残留,针对这一情况,我们再次利用小波变换对分离后的信号进行再消噪,从而得到更好的分离信号,实现了含有噪声的超高斯与亚高斯混合信号的盲分离,通过实验仿真证明了算法的有效性。
Blind signal separation (BSS) is a separation process that extract a series of signal source from the mixed data on the mixing process is unknown (the so-called "blind") .The noise model study with blind signal separation issue has broad application prospects. In this paper, we propose an approach to blind source separation of linear mixtures of the signals that the observations are contaminated with Gaussian noise.
Firstly, we introduce the basic theory of independent component analysis, high order theory and the information theory, analyses the principle and characteristic of some classical algorithms.
Blind source separation algorithm usually assume that the source signals in the prior probability density function, and thus access to critical nuclear function, and then isolated from the mixed-signal source signal. However, the assumption that the probability density function and a real probability density function different, the source will not be the correct signal separation. By the general assumption that the probability density function of the kernel function can be isolated from separate sub-Gaussian signal or super-signals. To solve this problem, this paper based on information theory, based on information of great principle and natural gradient, a super-Gaussian and mixed-signal-Blind separation method. The method combined use of Gaussian function and hyperbolic secant square function and the product of the combination of two Gaussian function of the signal source to estimate the probability density function, the peak of the information used as a parameter to choose probability density and the nonlinear model Function. But this method because of the white constraint conditions, so the number of non-stationary signals exist Stability, in order to eliminate this albino and bound algorithm to a number of non-stationary signals is unstable, and the albino relax restrictive conditions (known as incomplete constraints).
In the presence of noise, the general blind separation algorithm will not get good results, in this paper, the wavelet transform and the method of combining containing Gaussian noise mixed-signal separation. First of mixed signals to deal with noise, but when a eliminate noising can not be too thorough, to the extent possible, does not damage a useful observation signal components, but the problem is that this separation signal there will be significant residual noise. In view of this situation, we are once again using the wavelet transform the separation signal to noise elimination, and thus be better signal separation, the method effectively realize the contained noise of the super-Gaussian and mixed-signal Blind Separation, through simulation proved the effectiveness of the algorithm.
引文
[1]Karhunen J,Hyvarinen A.Application of neural blind separation to signal and image processing[J].in Proc ICASSP,1997,24(2):131-134.
[2]Makeig S,Jung TP,Bell A J.blind separation of auditory event-related brain responses into independen components[J].in Proc Natl Acad Sci,1997,94(3):10979-10984.
[3]J. Herault and C.Jutten.Space or Time Adaptive Signal Processing by Neural Network Models[J]. Neural Network for Computing: AIP Conference Proceedings,1986,18(4):241-256.
[4]C.Jutten and J.Herault. Blind Separation of Source[J].Signal Processing, 1991,32(1):24-110.
[5]J.Karhunen and J.Joutsensalo. Representation and Separation of Signal using Nonlinear PCA Type Learning[J]. Neural networks,1994, 7(1):113-127.
[6]Cichocki, R.Unbehauen and E.Rummert. Robust Learning Algorithm for Blind Separation of Signals[J]. Electronics letter, 1994, 30(17): 1386-1387.
[7]Comon.P. Independent Component Analysis A New Concept[J]. Signal Processing,1994,36(3): 287-314.
[8]R.Linsker. Local Synaptic Learning Rules Suffice to Maximize Mutual Information in A Linear Network[J]. Neural Computation, 1992, 4(1):691-702.
[9]A.J.Bell,Sejnowski Terrence d.An Information-Maximization Approach to Blind Separation and Blind Deconvolution[J]. Neural Computation, 1995, 7(6): 1004-1034.
[10]S.T.Amari, A.Cichocki, and H.H.Yang. A New Learning Algorithm for Blind Signal Separation[J]. Neural Information Processing Systems,1996, 8(2):757-763.
[11]D.T.Pham, P Garat. Blind Separation of a Mixture of Independent Sources through a Quasi-Maximum Likelihood Approach[J]. Signal Processing,1997, 45(7): l 712-1725.
[12]J.F.Cardoso.informax and Maximum Likelihood for blind source separation.Signal Processing letter,1997, 4(4): 112-114.
[13]M.Girolami and C. Fyfe, Generalized. Independent componentAnalysis through Unsupervised Learning with Emergent Bussgang Properties[J]. In Proceeding of Interneational Conference on Neural networks (1CCN), 1997,36(6), 1788-1791.
[14]T.W.Lee.Independent Component Analysis-Theory and Applications[M].New York:Kluwer Academic Publishers, 1998:26-78.
[15]T.W.Lee, M.Girolami, and T.J.Ssjnowski. Independent Component Analysis Using an Emend Informax Algorithm for Mixed Sub-Gaussian and Super-Gaussian Sources[M]. New York :Neural computation , 1998: 14-75.
[16]D.Yellin and E.Weinstein.Multichannel Signal Separation: Methods and Analysis[J]. IEEE Tansactions on Signal Pressing, 1996, 44(1):65-71.
[17] Hyvarinen.Independent Component Analysis In The Presence of Gaussian Noise by Maximizing Joint Likelihood[J]. Neurol computing, 1998, 22(2):49-67.
[18] E.Moulines, J.F .Cardoso, and E.Gassiat. Maximum Likelihood for Blind Separation and Deconvolution of Noisy Signals Using Mixture Models[J], In Processing of IEEE international Conference on Acoustics Speech, And Signal Processing,1997,47(6)3617-3620.
[19]Andrzej CICHOCK and Amari.Adaptive Blind Signal and Image Processing[M].北京:电子工业出版社,2005:163-166
[20]A.Cichpcki,J.Karhunen,W.Kasprrzak and R.Vigario.Neural Networks for Blind Separation with Unknown Numbei of Sources[J].Neurocomputin,1999,24(1):55-93.
[21]L.Q.Zhang,A. Cichocki,and S.Amari. Natural Gradient Algorithm for Blind Separation of Over determined Mixture with Additive Noise[J]. IEEE Signal Processing Letters, 1999, 6(11):293-295.
[22]Cao X R,Liu R W.General approach to blind source separation[J]. IEEE Trans on Signal Processing,1996,44(8):562-571.
[23].吴正国,夏立,尹为民.现代信号处理技术[M].武汉:武汉大学出版,2003:23-65.
[24]孟庆生.信息论[M].西安:西安交大出版社,1986:12-28.
[25].J.F.Cardoso. Higher-order Contrasts for Independent Component Analysis[J].Neural computation,1999, 11(3):157-192.
[26].A. Hyvarinen, E. Oja. A Fast Fix-point Algorithm for Independent Component Analysis[J]. Neural computation,1997, 9(1):1483-1492.
[27]杨福生,洪波.独立分量分析的原理与应用[M].北京:清华大学出版社,2006:68-69.
[28] S.Makeig, A.J.Bell, t.Jung, and T.J.Sejnowski.Independent Component Analysis of Electroencephagraphic Data[J].In Advances in Neural Information Processing system,1996,8(2): 145-151.
[32]Van Der Veen A,J.Algebraic Methods for Deterministic Blind Beam forming[J].IEEE Proc, 1998,86(10):1987-2008.
[30]马建仓,牛奕龙,陈海洋.盲信号处理[M].长沙:国防工业出版社,2006:91-92.
[31]杨行峻,郑君里.人工神经网络与盲信号处理[M].北京:清华大学出版社,2003:1-76.
[32]王亮.超高斯与亚高斯混合信号的盲分离研究[J].科学技术与工程,2006,6(18):1071-1815.
[33]牛龙,马建仓.一种新的基于峰度的盲源分离开关算法[J].系统仿真学报,2005,17(1):185-206.
[34]赵彩华,刘琚,孙建德,闫华.基于小波变换和独立分量分析的含噪混叠语音盲分离[J].电子与信息学报,2006,28(9):1565-1568.
[35]彭玉华.小波变换与工程应用[M].北京:科学出版社,1999:59-63.
[36]秦前清,杨宗凯.实用小波分析[M].西安:西安电子科技大学出版社,2001:14-59.
[37]李建平.小波分析与信号处理[M].重庆:重庆出版社,2001:12-48.
[38]皇甫堪,陈建文.现代数字信号处理[M].北京:电子工业出版社, 2003:339-366.
[39]M.Jansen.Wavelet threshold and noise reduction[M].Bristol:University of Bristol, 2000:23-47.
[40]Taswell.C.The what, Science&l:.agineeriag, 2000, how and why of wavelet shrinkage de-noising. 1n: Computing in23, 1219.
[41] Charnbolle A,1Je Vore, R. A, et al. Nonlinear wavelet image processing: vaiiational problems, compression, and noise removal through wavelet shrinkage.1n: IEEE Traps. On Gnage Processing, 1998, 73, 319.335.
[42] Moulin P, Liu Juan. Analysis of multiresolution image denoising schemes using genegaussian and complexity priors. In:正EE Trans. Information Theory, 1999, 45, 90}m919.
[43] Chang S q Yu Bin, Vetterlim. Adaptive wavelet thresholding for imap;e denoising andion. In: IEEE Trans. Image Processing, 2000,9(9),1532-.1546.
[44]Zhang Xiao Ping, Desai M D.Adaptive denoising based on SURE risk.In:IEEE SignalProcessing Letters,1985, 5(10), 265267.
[45]徐晨,赵瑞珍,甘小冰.小波分析与应用算法[M].北京:科学出版,2004:24-65
[2]Makeig S,Jung TP,Bell A J.blind separation of auditory event-related brain responses into independen components[J].in Proc Natl Acad Sci,1997,94(3):10979-10984.
[3]J. Herault and C.Jutten.Space or Time Adaptive Signal Processing by Neural Network Models[J]. Neural Network for Computing: AIP Conference Proceedings,1986,18(4):241-256.
[4]C.Jutten and J.Herault. Blind Separation of Source[J].Signal Processing, 1991,32(1):24-110.
[5]J.Karhunen and J.Joutsensalo. Representation and Separation of Signal using Nonlinear PCA Type Learning[J]. Neural networks,1994, 7(1):113-127.
[6]Cichocki, R.Unbehauen and E.Rummert. Robust Learning Algorithm for Blind Separation of Signals[J]. Electronics letter, 1994, 30(17): 1386-1387.
[7]Comon.P. Independent Component Analysis A New Concept[J]. Signal Processing,1994,36(3): 287-314.
[8]R.Linsker. Local Synaptic Learning Rules Suffice to Maximize Mutual Information in A Linear Network[J]. Neural Computation, 1992, 4(1):691-702.
[9]A.J.Bell,Sejnowski Terrence d.An Information-Maximization Approach to Blind Separation and Blind Deconvolution[J]. Neural Computation, 1995, 7(6): 1004-1034.
[10]S.T.Amari, A.Cichocki, and H.H.Yang. A New Learning Algorithm for Blind Signal Separation[J]. Neural Information Processing Systems,1996, 8(2):757-763.
[11]D.T.Pham, P Garat. Blind Separation of a Mixture of Independent Sources through a Quasi-Maximum Likelihood Approach[J]. Signal Processing,1997, 45(7): l 712-1725.
[12]J.F.Cardoso.informax and Maximum Likelihood for blind source separation.Signal Processing letter,1997, 4(4): 112-114.
[13]M.Girolami and C. Fyfe, Generalized. Independent componentAnalysis through Unsupervised Learning with Emergent Bussgang Properties[J]. In Proceeding of Interneational Conference on Neural networks (1CCN), 1997,36(6), 1788-1791.
[14]T.W.Lee.Independent Component Analysis-Theory and Applications[M].New York:Kluwer Academic Publishers, 1998:26-78.
[15]T.W.Lee, M.Girolami, and T.J.Ssjnowski. Independent Component Analysis Using an Emend Informax Algorithm for Mixed Sub-Gaussian and Super-Gaussian Sources[M]. New York :Neural computation , 1998: 14-75.
[16]D.Yellin and E.Weinstein.Multichannel Signal Separation: Methods and Analysis[J]. IEEE Tansactions on Signal Pressing, 1996, 44(1):65-71.
[17] Hyvarinen.Independent Component Analysis In The Presence of Gaussian Noise by Maximizing Joint Likelihood[J]. Neurol computing, 1998, 22(2):49-67.
[18] E.Moulines, J.F .Cardoso, and E.Gassiat. Maximum Likelihood for Blind Separation and Deconvolution of Noisy Signals Using Mixture Models[J], In Processing of IEEE international Conference on Acoustics Speech, And Signal Processing,1997,47(6)3617-3620.
[19]Andrzej CICHOCK and Amari.Adaptive Blind Signal and Image Processing[M].北京:电子工业出版社,2005:163-166
[20]A.Cichpcki,J.Karhunen,W.Kasprrzak and R.Vigario.Neural Networks for Blind Separation with Unknown Numbei of Sources[J].Neurocomputin,1999,24(1):55-93.
[21]L.Q.Zhang,A. Cichocki,and S.Amari. Natural Gradient Algorithm for Blind Separation of Over determined Mixture with Additive Noise[J]. IEEE Signal Processing Letters, 1999, 6(11):293-295.
[22]Cao X R,Liu R W.General approach to blind source separation[J]. IEEE Trans on Signal Processing,1996,44(8):562-571.
[23].吴正国,夏立,尹为民.现代信号处理技术[M].武汉:武汉大学出版,2003:23-65.
[24]孟庆生.信息论[M].西安:西安交大出版社,1986:12-28.
[25].J.F.Cardoso. Higher-order Contrasts for Independent Component Analysis[J].Neural computation,1999, 11(3):157-192.
[26].A. Hyvarinen, E. Oja. A Fast Fix-point Algorithm for Independent Component Analysis[J]. Neural computation,1997, 9(1):1483-1492.
[27]杨福生,洪波.独立分量分析的原理与应用[M].北京:清华大学出版社,2006:68-69.
[28] S.Makeig, A.J.Bell, t.Jung, and T.J.Sejnowski.Independent Component Analysis of Electroencephagraphic Data[J].In Advances in Neural Information Processing system,1996,8(2): 145-151.
[32]Van Der Veen A,J.Algebraic Methods for Deterministic Blind Beam forming[J].IEEE Proc, 1998,86(10):1987-2008.
[30]马建仓,牛奕龙,陈海洋.盲信号处理[M].长沙:国防工业出版社,2006:91-92.
[31]杨行峻,郑君里.人工神经网络与盲信号处理[M].北京:清华大学出版社,2003:1-76.
[32]王亮.超高斯与亚高斯混合信号的盲分离研究[J].科学技术与工程,2006,6(18):1071-1815.
[33]牛龙,马建仓.一种新的基于峰度的盲源分离开关算法[J].系统仿真学报,2005,17(1):185-206.
[34]赵彩华,刘琚,孙建德,闫华.基于小波变换和独立分量分析的含噪混叠语音盲分离[J].电子与信息学报,2006,28(9):1565-1568.
[35]彭玉华.小波变换与工程应用[M].北京:科学出版社,1999:59-63.
[36]秦前清,杨宗凯.实用小波分析[M].西安:西安电子科技大学出版社,2001:14-59.
[37]李建平.小波分析与信号处理[M].重庆:重庆出版社,2001:12-48.
[38]皇甫堪,陈建文.现代数字信号处理[M].北京:电子工业出版社, 2003:339-366.
[39]M.Jansen.Wavelet threshold and noise reduction[M].Bristol:University of Bristol, 2000:23-47.
[40]Taswell.C.The what, Science&l:.agineeriag, 2000, how and why of wavelet shrinkage de-noising. 1n: Computing in23, 1219.
[41] Charnbolle A,1Je Vore, R. A, et al. Nonlinear wavelet image processing: vaiiational problems, compression, and noise removal through wavelet shrinkage.1n: IEEE Traps. On Gnage Processing, 1998, 73, 319.335.
[42] Moulin P, Liu Juan. Analysis of multiresolution image denoising schemes using genegaussian and complexity priors. In:正EE Trans. Information Theory, 1999, 45, 90}m919.
[43] Chang S q Yu Bin, Vetterlim. Adaptive wavelet thresholding for imap;e denoising andion. In: IEEE Trans. Image Processing, 2000,9(9),1532-.1546.
[44]Zhang Xiao Ping, Desai M D.Adaptive denoising based on SURE risk.In:IEEE SignalProcessing Letters,1985, 5(10), 265267.
[45]徐晨,赵瑞珍,甘小冰.小波分析与应用算法[M].北京:科学出版,2004:24-65