多种混合模型下的盲信号分离方法研究
|
摘要
盲信号分离（Blind Signal Separation，BSS）是指仅通过对传感器上获取的一组观测信号进行分析和处理，从而在并不了解混合系统先验信息的情况下恢复出无法直接观测的多维源信号。盲信号分离在无线通信，语音的识别和增强，图像的重构和特征提取等方面都有着广泛而重要的应用价值，使得其已成为近年来人工神经网络，统计学以及信号处理等相关科研领域所研究的一个热点问题。本文围绕多种混合模型情况下的盲信号分离问题，做了以下几个方面的工作：
首先，对于线性适定混合模型，即源信号数目与观测信号数目相等的情况，基于最小化互信息原理，分别提出了两种自适应BSS方法。针对传统的梯度类BSS算法在实时计算中收敛速度较慢的问题，提出了一种基于动量项技术的BSS算法。该算法采用分离信号的互信息量作为代价函数，并将动量项融入到了优化该代价函数的自然梯度学习规则中，推导了搜索期望分离矩阵的自适应算法。为了使得所提算法能够分离出包含不同统计特性的源信号，在分离算法的每一步迭代更新中，使用了基于Gram-Charlier展开式的分离信号评价函数的估计算法。仿真结果验证了所提BSS算法在收敛速度上的优越性，以及在源信号中同时包含超高斯和亚高斯信号时的分离性能。
鉴于共轭梯度算法在神经网络学习中所表现出的卓越性能，提出了一种基于共轭梯度的自适应盲信号分离算法。该算法在传统的随机梯度和自然梯度算法的基础上，结合互信息准则，将共轭梯度搜索原理引入到了最优分离矩阵的求解中。即分离矩阵总是沿着与当前搜索方向共轭的方向进行更新。作为算法成功与否的关键点，采用核概率密度估计方法来估计分离信号的概率密度，进而直接估计出对应的评价函数，而不是依据经验来选取单一的非线性函数。仿真结果验证了基于共轭梯度的BSS算法的有效性。
对于传感器接收的观测信号数目多于源信号，且混合矩阵为列满秩矩阵的情形，提出了一种快速收敛的超定盲信号分离方法。该方法从对分离矩阵进行奇异值分解入手，引入了超定BSS的代价函数。然后依据该代价函数，利用共轭梯度搜索原理推导了迭代计算分离矩阵的学习算法。并在算法的每一步计算中，利用随机变量概率密度函数的核密度估计法估计分离信号的评价函数。在计算机仿真中，通过与随机梯度算法和自然梯度算法相比较，验证了所提超定BSS算法的性能。
针对欠定混合模型中观测信号数量不足的问题，研究了在欠定混合条件下的非稀疏信号的BSS问题，提出了一种基于局部平均分解的欠定混合BSS方法。该方法的基本思想是首先通过对混合信号进行局部平均分解处理，生成若干乘积函数。按照一定的标准挑选出足够数目的乘积函数，进而构造出一组额外的混合信号。将该组信号加入到原来的混合信号中，使得欠定盲分离模型转变为适定或超定盲分离模型以便于处理。对于新的混合信号和新的混合模型，使用两种高效的盲分离算法分离出源信号。理论上，局部平均分解算法的应用对于信号的类别是没有限制的。因此，所提的欠定盲分离算法可以打破大多数方法中存在的稀疏性约束，适用范围更广。另一方面，所提算法直接计算源信号，而不用预先估计出欠定混合矩阵，免去了不必要的计算。仿真结果验证了算法的性能。
除了上述线性混合模型以外，对于非线性混合模型，提出了一种基于感知器网络的非线性盲信号分离方法。该方法采用感知器网络构建非线性分离系统来分离源信号，以最大输出信息熵原理作为分离准则调整非线性分离系统的参数，利用共轭梯度优化算法计算分离感知器的隐层和输出层连接权矩阵。算法中的Sigmoid函数选为分离信号的概率分布函数，并采用一种自适应参数化概率密度估计方法对其进行估计。仿真结果验证了所提算法的有效性。
最后，提出了一种用于线性卷积混合信号盲分离的联合对角化方法。当信号的混合过程并不是瞬时完成，也就是在将源信号到传感器的传输过程中的延时也考虑进去的时候，盲信号分离问题的混合模型就变成了一个多维信号的卷积混合模型。所提的BSS方法首先将卷积混合模型变换为瞬时混合模型，得到新的瞬时混合信号，然后对变换后的模型应用联合对角化技术求取分离矩阵。同时，仿真结果表明该方法可成功实现线性卷积混合信号的盲分离。
Blind Signal Separation (BSS) is defined as retrieving the potential unobservablemultidimensional source signals just from a set of observation signals received by a group ofsensors, without knowing a prior knowledge of the transmitting system. Recently, BlindSignal Separation has become a hot issue in the scientific fields of statistics, neural networksand signal proeessing, due to its wide and important application perspective in wirelesscommunication, speech identification and enhancement, image recognition and featureextraction, etc. For the BSS problems under different mixing models, the main contributionsof this dissertation are as follows:
First, for the typical linear determined mixing model, i.e., the number of the observationsignals is equal to the number of the source signals, two adaptive blind signal separationmethods are proposed separately based on the Minimum Mutual Information principle. Forthe relatively slow convergence problem of the traditional gradient-type algorithm in thereal-time computation, a new BSS algorithm is presented with the momentum technology.The proposed algorithm adopts the mutual information of the separation signals as the costfunction. The momentum is incorporated into the natural gradient updating rules foroptimizing the cost function, and then an adaptive learning algorithm for searching theoptimal separating matrix is derived. In order to enable the proposed algorithm to separate thesource signals with different statistical properties, in each updating step, an online scorefunction estimation method based on the Gram-Charlier expansion is employed. Simulationresults validate the fast convergent speed and the appealing behavior in separating the sourceswith both Super-Gaussian and the Sub-Gaussian signals of the proposed adaptive BSSmethod.
In consideration of the appealing performance of the conjugate gradient optimizationalgorithm in the neural network training, a new adaptive blind signal separation algorithm isproposed based on the conjugate gradient. On the basis of the stochastic gradient algorithmand the natural gradient one, the proposed BSS algorithm introduces the conjugate gradientsearching principle to calculate the expected separating matrix, combining the mutualinformation criterion. In other words, the separating matrix always updates along the directionconjugate to the current searching direction. As a keypoint of the algorithm, a kernel densityfunction estimation method is exploited to estimate probability density function and itsderivative of the separating signals, instead of choosing a certain non-linear functionempirically. Simulation results confirm the effectiveness of the proposed conjugate gradientbased BSS method.
For the case, when there are more observation signals than the source signals, and themixing matrix has full column rank, an over-determined BSS algorithm is presented. Thealgorithm first introduces an over-determined BSS cost function based on the singular valuedecomposition on the separating matrix. Then the learning algorithm of the separating matrixis derived with the conjugate gradient searching principle. The score functions are estimated by the kernel density function estimation. Simulations demonstrate the superior performanceof the proposed algorithm through comparison with the traditional stochastic gradient and thenatural algorithm.
For the problem of the insufficient number of the observation signals under theunderdetermined mixing model, a new underdetermined BSS method is proposed based onthe local mean decomposition technology. The BSS problem for non-sparse signals under theunderdetermined mixing model is studied. The propsoed BSS method firstly introduces thelocal mean decomposition algorithm into the underdetermined BSS model to generate severalproduct functions, which are then filtrated in the light of a certain criterion. The selectedproduct functions are then combined with the initial mixtures such that the underdeterminedBSS problem is transformed into a determined one which is much easier to cope with, and thedifficulty of the deficiency of the mixtures is overcome. For the rebuilt mixtures and thenewly formed determined BSS problem, two BSS algorithms are proposed to recover thesources. Theoretically, there is no limit to the object of the LMD algorithm, so the proposedunderdetermined BSS method is supposed to be able to break the sparse constraint included inmost existed methods. On the other hand, the proposed BSS method separates the sourcesignals directly, instead of estimating the underdetermined mixing matrix primarily, avoidingthe unnecessary computation. Simulations results show the good performance of the proposedmethod.
In addition to the above mentioned linear mixing model, the non-linear BSS problem isalso investigated. A non-linear BSS method based on perceptron network is proposed. Themethod employs a three layer perceptron network as the non-linear separating system. TheInformax principle is exploited as the basis to search for the optimal parameters of thenon-linear separating system. The conjugate gradient algorithm is used to update the weightmatrices of the hide layer and the output layer of the perceptron system to speed up theconvergence of the BSS algorithm. Additionally, the probability density function is chosen asthe Sigmoid function in the algorithm, and is estimated adaptively by a parametric method.Simulations results confirm the appealing performance of the proposed non-linear BSSmethod.
Finally, a new blind signal separation method based on joint approximate diagonalizationis proposed for the linear convolutive mixing model. If the mixing process is notinstantaneous, i.e., the time delay is also considered during the transmitting process from thesources to the sensors, the BSS problem will become a multidimensional convolutive mixingmodel. In the proposed BSS method, the convolutive mixing model is first transformed intoan instantaneous mixing model; then a joint approximate diagonalization method is applied tothe transformed model in order to computing out the separating matrix. Meanwhile, in theprocess of diagonalization, a constraint condition is introduced for the limitation of the classof the separating matrices such that the singular solutions are avoided. Simulation resultsshow that the proposed method can realize the blind separation of convolutive mixture signals successfully.
首先，对于线性适定混合模型，即源信号数目与观测信号数目相等的情况，基于最小化互信息原理，分别提出了两种自适应BSS方法。针对传统的梯度类BSS算法在实时计算中收敛速度较慢的问题，提出了一种基于动量项技术的BSS算法。该算法采用分离信号的互信息量作为代价函数，并将动量项融入到了优化该代价函数的自然梯度学习规则中，推导了搜索期望分离矩阵的自适应算法。为了使得所提算法能够分离出包含不同统计特性的源信号，在分离算法的每一步迭代更新中，使用了基于Gram-Charlier展开式的分离信号评价函数的估计算法。仿真结果验证了所提BSS算法在收敛速度上的优越性，以及在源信号中同时包含超高斯和亚高斯信号时的分离性能。
鉴于共轭梯度算法在神经网络学习中所表现出的卓越性能，提出了一种基于共轭梯度的自适应盲信号分离算法。该算法在传统的随机梯度和自然梯度算法的基础上，结合互信息准则，将共轭梯度搜索原理引入到了最优分离矩阵的求解中。即分离矩阵总是沿着与当前搜索方向共轭的方向进行更新。作为算法成功与否的关键点，采用核概率密度估计方法来估计分离信号的概率密度，进而直接估计出对应的评价函数，而不是依据经验来选取单一的非线性函数。仿真结果验证了基于共轭梯度的BSS算法的有效性。
对于传感器接收的观测信号数目多于源信号，且混合矩阵为列满秩矩阵的情形，提出了一种快速收敛的超定盲信号分离方法。该方法从对分离矩阵进行奇异值分解入手，引入了超定BSS的代价函数。然后依据该代价函数，利用共轭梯度搜索原理推导了迭代计算分离矩阵的学习算法。并在算法的每一步计算中，利用随机变量概率密度函数的核密度估计法估计分离信号的评价函数。在计算机仿真中，通过与随机梯度算法和自然梯度算法相比较，验证了所提超定BSS算法的性能。
针对欠定混合模型中观测信号数量不足的问题，研究了在欠定混合条件下的非稀疏信号的BSS问题，提出了一种基于局部平均分解的欠定混合BSS方法。该方法的基本思想是首先通过对混合信号进行局部平均分解处理，生成若干乘积函数。按照一定的标准挑选出足够数目的乘积函数，进而构造出一组额外的混合信号。将该组信号加入到原来的混合信号中，使得欠定盲分离模型转变为适定或超定盲分离模型以便于处理。对于新的混合信号和新的混合模型，使用两种高效的盲分离算法分离出源信号。理论上，局部平均分解算法的应用对于信号的类别是没有限制的。因此，所提的欠定盲分离算法可以打破大多数方法中存在的稀疏性约束，适用范围更广。另一方面，所提算法直接计算源信号，而不用预先估计出欠定混合矩阵，免去了不必要的计算。仿真结果验证了算法的性能。
除了上述线性混合模型以外，对于非线性混合模型，提出了一种基于感知器网络的非线性盲信号分离方法。该方法采用感知器网络构建非线性分离系统来分离源信号，以最大输出信息熵原理作为分离准则调整非线性分离系统的参数，利用共轭梯度优化算法计算分离感知器的隐层和输出层连接权矩阵。算法中的Sigmoid函数选为分离信号的概率分布函数，并采用一种自适应参数化概率密度估计方法对其进行估计。仿真结果验证了所提算法的有效性。
最后，提出了一种用于线性卷积混合信号盲分离的联合对角化方法。当信号的混合过程并不是瞬时完成，也就是在将源信号到传感器的传输过程中的延时也考虑进去的时候，盲信号分离问题的混合模型就变成了一个多维信号的卷积混合模型。所提的BSS方法首先将卷积混合模型变换为瞬时混合模型，得到新的瞬时混合信号，然后对变换后的模型应用联合对角化技术求取分离矩阵。同时，仿真结果表明该方法可成功实现线性卷积混合信号的盲分离。
Blind Signal Separation (BSS) is defined as retrieving the potential unobservablemultidimensional source signals just from a set of observation signals received by a group ofsensors, without knowing a prior knowledge of the transmitting system. Recently, BlindSignal Separation has become a hot issue in the scientific fields of statistics, neural networksand signal proeessing, due to its wide and important application perspective in wirelesscommunication, speech identification and enhancement, image recognition and featureextraction, etc. For the BSS problems under different mixing models, the main contributionsof this dissertation are as follows:
First, for the typical linear determined mixing model, i.e., the number of the observationsignals is equal to the number of the source signals, two adaptive blind signal separationmethods are proposed separately based on the Minimum Mutual Information principle. Forthe relatively slow convergence problem of the traditional gradient-type algorithm in thereal-time computation, a new BSS algorithm is presented with the momentum technology.The proposed algorithm adopts the mutual information of the separation signals as the costfunction. The momentum is incorporated into the natural gradient updating rules foroptimizing the cost function, and then an adaptive learning algorithm for searching theoptimal separating matrix is derived. In order to enable the proposed algorithm to separate thesource signals with different statistical properties, in each updating step, an online scorefunction estimation method based on the Gram-Charlier expansion is employed. Simulationresults validate the fast convergent speed and the appealing behavior in separating the sourceswith both Super-Gaussian and the Sub-Gaussian signals of the proposed adaptive BSSmethod.
In consideration of the appealing performance of the conjugate gradient optimizationalgorithm in the neural network training, a new adaptive blind signal separation algorithm isproposed based on the conjugate gradient. On the basis of the stochastic gradient algorithmand the natural gradient one, the proposed BSS algorithm introduces the conjugate gradientsearching principle to calculate the expected separating matrix, combining the mutualinformation criterion. In other words, the separating matrix always updates along the directionconjugate to the current searching direction. As a keypoint of the algorithm, a kernel densityfunction estimation method is exploited to estimate probability density function and itsderivative of the separating signals, instead of choosing a certain non-linear functionempirically. Simulation results confirm the effectiveness of the proposed conjugate gradientbased BSS method.
For the case, when there are more observation signals than the source signals, and themixing matrix has full column rank, an over-determined BSS algorithm is presented. Thealgorithm first introduces an over-determined BSS cost function based on the singular valuedecomposition on the separating matrix. Then the learning algorithm of the separating matrixis derived with the conjugate gradient searching principle. The score functions are estimated by the kernel density function estimation. Simulations demonstrate the superior performanceof the proposed algorithm through comparison with the traditional stochastic gradient and thenatural algorithm.
For the problem of the insufficient number of the observation signals under theunderdetermined mixing model, a new underdetermined BSS method is proposed based onthe local mean decomposition technology. The BSS problem for non-sparse signals under theunderdetermined mixing model is studied. The propsoed BSS method firstly introduces thelocal mean decomposition algorithm into the underdetermined BSS model to generate severalproduct functions, which are then filtrated in the light of a certain criterion. The selectedproduct functions are then combined with the initial mixtures such that the underdeterminedBSS problem is transformed into a determined one which is much easier to cope with, and thedifficulty of the deficiency of the mixtures is overcome. For the rebuilt mixtures and thenewly formed determined BSS problem, two BSS algorithms are proposed to recover thesources. Theoretically, there is no limit to the object of the LMD algorithm, so the proposedunderdetermined BSS method is supposed to be able to break the sparse constraint included inmost existed methods. On the other hand, the proposed BSS method separates the sourcesignals directly, instead of estimating the underdetermined mixing matrix primarily, avoidingthe unnecessary computation. Simulations results show the good performance of the proposedmethod.
In addition to the above mentioned linear mixing model, the non-linear BSS problem isalso investigated. A non-linear BSS method based on perceptron network is proposed. Themethod employs a three layer perceptron network as the non-linear separating system. TheInformax principle is exploited as the basis to search for the optimal parameters of thenon-linear separating system. The conjugate gradient algorithm is used to update the weightmatrices of the hide layer and the output layer of the perceptron system to speed up theconvergence of the BSS algorithm. Additionally, the probability density function is chosen asthe Sigmoid function in the algorithm, and is estimated adaptively by a parametric method.Simulations results confirm the appealing performance of the proposed non-linear BSSmethod.
Finally, a new blind signal separation method based on joint approximate diagonalizationis proposed for the linear convolutive mixing model. If the mixing process is notinstantaneous, i.e., the time delay is also considered during the transmitting process from thesources to the sensors, the BSS problem will become a multidimensional convolutive mixingmodel. In the proposed BSS method, the convolutive mixing model is first transformed intoan instantaneous mixing model; then a joint approximate diagonalization method is applied tothe transformed model in order to computing out the separating matrix. Meanwhile, in theprocess of diagonalization, a constraint condition is introduced for the limitation of the classof the separating matrices such that the singular solutions are avoided. Simulation resultsshow that the proposed method can realize the blind separation of convolutive mixture signals successfully.
引文
[1] Cichocki A, Amari S. Adaptive Blind Signal and Image Processing—Learning Algorithms andApplication [M]. New York: John Wiley&Sons,2003.1–40.
[2] Choi S, Cichocki A, Park H M, Lee S Y. Blind source separation and independent component analysis:A review [J]. Neural Inf. Process.,2005,6(1):1–57.
[3]张发启,张斌,张喜斌.盲信号处理及应用[M].西安：西安电子科技大学出版社,2006.1–30.
[4]杨竹青,李勇,胡德文.独立成分分析方法综述[J].自动化学报,2002,28(5):762–772.
[5] Hyv rinen A, Karhunen J, Oja E. Independent Component Analysis [M]. New York: John Wiley&Sons,2001.
[6] Khaliq A A, Qureshi I M, Shaha J A. Source extraction from functional magnetic resonance imagingdata using ICA based on fourth-order and exponential contrast functions [J]. J. Chin. Inst. Eng.2013,36(6):730–742.
[7] Ye Y, Zhang Z L, Zeng J, Peng L. A fast and adaptive ICA algorithm with its application to fetalelectrocardiogram extraction [J]. Appl. Math. Comput.,2008,205(2):799–806.
[8] Georgiev P, Theis F, Cichocki A. Sparse component analysis and blind source separation ofunderdetermined mixtures [J]. IEEE Trans. Neural Netw.,2005,16(4):992–996.
[9] Li Y Q, Cichocki A, Amari S. Analysis of sparse representation and blind source separation [J]. NeuralComputation,2004,16(6):1193–1234.
[10] Zhang H, Li L, Li W. Independent vector analysis for convolutive blind noncircular source separation[J]. Signal Process.,2012,92(9):2275–2283.
[11] Attias H. Independent factor analysis [J]. Neural Computation,1999,11:803–851.
[12]张俊萍,刘爱伦.基于独立因子分析法的信号盲分离的应用[J].华东理工大学学报(自然科学版),2008,34(3):410–416.
[13] Antoni J. Blind separation of vibration components: principles and demonstrations [J]. Mech. Syst.Signal Process.,2005,19:1166–1180.
[14] Kociński J, Drgas S, Ozimek E. Evaluation of blind source separation for different algorithms basedon second order statistics and different spatial configurations of directional microphones [J]. Appl.Acoust.,2012,73(2):109–116.
[15] Maazouzi F, Bahi Halima. Type-2Fuzzy Gaussian mixture models for singing voice classification incommercial music production [J]. Int. J. Signal Imag. Syst. Engineer.,2013,6(2):111–118.
[16] Wang F, Li H, Li R. Harmonic signals retrieval approach based on blind source separation [J]. Circ.,Syst. Signal Process.,2010,29(4):669–685.
[17]罗一涵,付承毓.基于中频的实时图像盲复原算法[J].四川大学学报(工程科学版),2010,42(6):109–118.
[18] Naceur M, Loghmari M, Boussema M. The contribution of the sources separation method in thedecomposition of mixed pixels [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(2):2642–2653.
[19] Kolba J, Jouny I. Blind source separation in tumor detection in mammograms [C]. In: Proc. of theIEEE32nd Annual Northeast Bioengineering Conference. New York: IEEE Press,2006.65–66.
[20] Congedo M, Pailler C G, Jutten C. On the blind source separation of human electroencephalogram byapproximate joint diagonalization of second order statistic [J]. Clinical Neurophysiology,2008,199(12):2677–2686.
[21] Guo X, Chang C, Lam Y. Blind separation of electron paramagnetic resonance signals using diversityminimization [J]. J. Magn. Reson.,2010,204(1):26–36.
[22] Sun Y, Ridge C, Rio F, Shaka A J, Xin J. Postprocessing and sparse blind source separation of positiveand partially overlapped data [J]. Signal Process.,2011,91(8):1838–1851.
[23] Pauca V P, Shahnaz F, Berry W, Plemmons R J. Text mining using nonnegative matrix factorizations[C]. In: Proc. of the4th SIAM International Conference on Data Mining (ICDM-2004),2004.452–456.
[24]张安清,邱天爽.波束域的信号盲分离方法[J].系统工程与电子技术,2008,30(9):1628–1631.
[25] Budipriyanto A. Blind source separation based dynamic parameter identification of a multi-storymoment-resisting frame building under seismic ground motions [J]. Procedia Engineer.,2013,54:299–307.
[26] Lathauwer L D, Castaing J. Tensor-based techniques for the blind separation of DS-CDMA signals [J].Signal Process.,2007,87(2):322–336.
[27]杨祖元.盲信号分离算法分析应用研究[D].[博士学位论文].广州:华南理工大学电子与信息学院,2009.
[28] Jutten C, Herault J. Blind separation of source part I: an adaptive algorithm based on neuromimeticarchitecture [J]. Signal Process.,1991,24:1–10.
[29] Comon P. Independent component analysis, a new concept?[J]. Signal Process.,1994,36:287–314.
[30] Cao X R, Liu R. General approach to blind source separation [J]. IEEE Trans. Signal Process.,1996,44(3):562–571.
[31] Hyv rinen A. The FastICA MATLAB package [EB/OL]. http://www.cis.hut.fi/projects/ica/fastica,2013-12-21.
[32] Novey M, Adali T. On extending the complex FastICA algorithm to noncircular sources [J]．IEEETrans. Signal Process.,2008,56(5):2148–2154.
[33] Zarzoso V, Comon P. Robust Independent component analysis by iterative maximization of thekurtosis contrast with algebraic optimal step size [J]. IEEE Trans. Neural Netw.,2010,21(2):248–261.
[34] Wang Y, Y lmaz, Zhou Z. Phase aliasing correction for robust blind source separation using DUET[J]. Appl. Comput. Harmonic Anal.,2013,35(2):341–349.
[35] Cardoso J F, Souloumiac A. Jacobi angles for simultaneous diagonalization [J]. SIAM J. Matrix Anal.Appl.,1996,17(1):161–164.
[36] Belouchrani A, Abed-Meraim K, Cardoso J F. A blind source separation technique using second-orderstatistics [J]. IEEE Trans. Signal Process.,1997,45(2):434–444.
[37] Joho M, Mathis H. Joint diagonalization of correlation matrices by using gradient methods withapplication to blind signal separation [C]. In: Proc. of IEEE Sensor Array and Multichannel SignalProcessing Workshop. New York: IEEE Press,2002.273–277.
[38] Moreau E. A generalization of joint diagonalization criteria for source separation [J]. IEEE Trans.Signal Process.,2001,49(3):530–541.
[39] Pham D.T. Joint approximate diagonalization of positive definite Hermitian matrices [J]. SIAM J.Matrix Anal. Appl.,2001,22(4):1136–1152.
[40] Van Der Veen A J. Joint diagonalization via subspace fitting techniques [C]. In: Proc. of IEEEInternational Conference on Acoustics, Speech, and Signal Processing (ICASSP-2001). New York:IEEE Press,2001.2773–2776.
[41] Souloumiac A. Nonorthogonal joint diagonalization by combining givens and hyperbolic rotations [J].IEEE Trans. Signal Process.,2009,57(6):2222–2231.
[42]张华,冯大政,聂卫科,徐先峰.非正交联合对角化盲源分离算法[J].西安电子科技大学学报(自然科学版),2008,35(1):27–31.
[43]李昌利,曹嘉毅.基于循环优化的矩阵联合对角化算法及在盲源分离中的应用[J].四川大学学报（工程科学版）,2011,43(5):159–162.
[44] Ye J M, Jin H H, Lou S T, You K J. An optimized EASI algorithm [J]. Signal Process.,2009,89(3):333–338.
[45] Liu D, Liu X. Informax algorithm based on linear ICA neural network for BSS problems [C]. In: Proc.of the4th World Congress on Intelligent Control and Automation (WCICA-2002),2002.1949–1952.
[46] Zhu X L, Zhang X D, Ding Z Z, Jia Y. Adaptive nonlinear PCA algorithms for blind source separationwithout prewhitening [J]. IEEE Trans. Circ. Syst.,2006,53(3):745–753.
[47]欧世峰,赵晓晖,高颖.结合辅助分离系统的变步长盲源分离算法[J].电子学报,2009,37(7):1588–1593.
[48]付卫红,杨小牛,刘乃安,曾兴雯.基于步长最优化的EASI盲源分离算法[J].四川大学学报(工程科学版),2008,40(1):118–121.
[49] Joho M, Mathis H, Lambert R H. Overdetermined blind source separation: using more sensors thansource signals in a noisy mixture [C]. In: Proc. of Independent Component Analysis and Blind SignalSeparation (ICA-2000).2000.81–86.
[50] Nishikawa T, Abe H, Saruwatari H, Shikano K. Overdetermined blind source separation of realacoustic sounds based on multistage ica using subarray processing [C]. In: Proc. of the3rdIEEEInternational Symposium on Signal Processing and Information Technology (ISSPIT-2003). NewYork: IEEE Press,2003.510–513.
[51] Amari S I. Natural gradient learning for over-and under-complete bases in ICA [J]. NeuralCornputation,1999,11(8):1875–1883.
[52] Zhang L Q, Cichocki A, Amari S I. Natural gradient algorithm for blind separation of overdeterminedmixture with additive noise [J]. IEEE Signal Process. Lett.,1999,6(11):293–295.
[53] Omlor L, Giese M A. Blind source separation for over-determined delayed mixtures [J]. Advances inNeural Information Processing Systems,2007,19:1074–1081.
[54] Duarte L T, Suyama R, Attux R, Deville Y, Romano J M T, Jutten C. Blind source separation ofoverdetermined linear-quadratic mixtures [C]. In: Vigneron V, Zarzoso V, Moreau E, Gribonval R,Vincent E.(eds.) Proc. of the9thInternational Conference on Latent Variable Analysis and SignalSeparation (LVA/ICA-2010). Berlin: Springer Berlin Heidelberg,6365:263–270.
[55] Lathauwer L D, Castaing J, Cardoso J F. Fourth-order cumulant-based blind identification ofunderdetermined mixtures [J]. IEEE Trans. Signal Process.,2007,55(6):2965–2973.
[56] Thomas J, Deville Y, Shahram H. Differential fast fixed-point algorithm for underdeterminedinstantaneous and convolutive partial blind source separation [J]. IEEE Trans. Signal Process.,2007,55(7):3717–3729.
[57] Bofill P, Zibulevsky M. Underdetermined blind source separation using sparse representations [J].Signal Process.,2001,81(11):2353–2362.
[58] Sadhu A, Hazra B, Narasimhan S. Decentralized modal identification of structures using parallelfactor decomposition and sparse blind source separation [J]. Mech. Syst. Signal Process.,2013,41(1-2):396–419.
[59] Lewicki M S, Sejnowski T J, Hughes H. Learning overcomplete representations [J]. NeuralComputation,2000,12:337–365.
[60] Zibulevsky M, Pearlmutter B A. Blind source separation by sparse decomposition in a signaldictionary [J]. Neural Computation,2001,13(4):863–882.
[61] Theis F J, Puntonet C G, Lang E W. Median-based clustering for underdetermined blind signalprocessing [J]. IEEE Signal Process. Lett.,2006,13(2):96–99.
[62] Thiagarajan J J, Ramamurthy K N, Spanias A. Mixing matrix estimation using discriminativeclustering for blind source separation [J]. Digital Signal Process.,2013,23(1):9–18.
[63] Linh-Trung N, Belouchrani A, Abed-Meraim K, Boashash B. Separating more sources than sensorsusing time-frequency distributions [J]. EURASIP J. Applied Signal Process.,2005,2005(17):2828–2847.
[64] Theis F., Lang E W, Puntonet C G. A geometric algorithm for overcomplete linear ICA [J].Neurocomputing,2004,56:381–398.
[65] Peng D, Xiang Y. Underdetermined blind separation of non-sparse sources using spatialtime-frequency distributions [J]. Digital Signal Process.,2010,20(2):581–596.
[66] Deville Y, Benali M, Abrard F. Differential source separation for underdetermined instantaneous orconvolutive mixtures: concept and algorithms [J]. Signal Process.,2004,84(10):1759–1776.
[67] Shi Z, Zhang C. Nonlinear innovation to blind source separation [J]. Neurocomputing,2007,71(1-3):406–410.
[68] Lin J K, Grier D G, Cowan J D. Source separation and density estimation by faithful equivariant SOM[C]. In: Proc. of Advances in Neural Information Processing Systems9(ANIPS-1997), MA: MITPress,1997.536–542.
[69] Almeida L B. MISEP-linear and nonlinear ICA based on mutual information [J]. J. Mach. Learn. Res.,2003,4:1297–1318.
[70] Almeida L B. Linear and nonlinear ICA based on mutual information-the MISEP method [J]. SignalProcess.,2004,84(2):231–245.
[71] Martinez D, Bray A. Nonlinear blind separation using kernels [J]. IEEE Trans. Nueral Netw.,2003,14(l):228–235.
[72] Solazzi M, Piazza F, Uneini A. Nonlinear blind source separation by spline neural networks [C]. In:Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-2001).New York: IEEE Press,2001,5:2781–2784.
[73] Milani F, Solazzi M, Uneini A. Blind source separation of convolutive nonlinear mixtures by flexiblespline nonlinear functions [C]. In: Proc. of IEEE International Conference on Acoustics, Speech, andSignal Processing (ICASSP-2002). New York: IEEE Press,2002,2:1641–1644.
[74] Honkela A, Valpola H, Ilin A, Karhunen J. Blind separation of nonlinear mixtures by variationalBayesian learning,Digital Signal Processing [J].2007,17(5):914–934.
[75] Song K, Ding M, Wang Q, Liu W. Blind source separation in post-nonlinear mixtures using naturalgradient descent and particle swarm optimization algorithm [C]. In: Proc. of Advances in NeuralNetworks, Lecture Notes in Computer Science (ISNN-2007),2007,4493:721–730.
[76]陶涛,黄高明,赵治华.后非线性混叠信号盲源分离算法综述[J].控制与决策,2010,25(8):1121–1128.
[77] Tan Y, Wang J, Zurada J. Nonlinear blind source separation using a radial basis function network [J].IEEE Trans. Neural Netw.,2001,12(1):124–134.
[78] Hosseini S, Deville Y. Recurrent networks for separating extractable-target nonlinear mixtures. Part II:blind configurations [J]. Signal Process.,2013,93(4):671–683.
[79] Deville Y, Hosseini S. Recurrent networks for separating extractable-target nonlinear mixtures. Part I:non-blind configurations [J]. Signal Process.,2009,89(4):378–393.
[80]楼红伟,胡光锐.基于小波域的非平稳卷积混合语音信号的自适应盲分离[J].控制与决策,2004,19(1):73–76.
[81] Dam H H, Cantoni A, Nordholm S, et al. Second order blind signal separation for convolutivemixtures using conjugate gradient [J]. IEEE Signal Process. Lett.,2008,15:79–82.
[82] Araki S, Mukai R, Makino S. The fundamental limitation of frequency domain blind sourceseparation for convolutive mixtures of speech [J]. IEEE Trans. Speech Audio Process.,2003,11(2):109–116.
[83] Parra L, Spence C. Convolutive blind separation of nonstationary sources [J]. IEEE Trans. SpeechAudio Process.,2000,8(3):320–327.
[84] Saruwatari H, Kawamura T, Nishikawa T, Lee A, Shikano K. Blind source separation based on afast-convergence algorithm combining ICA and beamforming [J]. IEEE Trans. Speech Audio Process.,2006,14(2):666–678.
[85] Murata N, Ikeda S, Ziehe A. An approach to blind source separation based on temporal structure ofspeech signals [J]. Neurocomputing,2001,41:1–24.
[86] Kawamoto M, Matsucka K, Ohnishi N. A method of blind separation for convolved non-stationarysignals [J]. Neurocomputing,1998,22(1-3):157–171.
[87] Bousbia S H, Belouchrani A, Abed M K. Blind separation of convolutive mixtures using joint blockdiagonalization [C]. In: Proc. of IEEE International Symposium on Signal Processing and itsApplications (ISSPA-2001). New York: IEEE Press,2001.13–16.
[88] Yellin D, Weinstein E. Multichannel signal separation: methods and analysis [J]. IEEE Trans. SignalProcess.,1996,44(1):106–118.
[89] Sun X, Douglas S C. Multichannel blind deconvolution of arbitrary signals: adaptive algorithms andstability analysis [C]. In: Proc. of the34thAsilomar Conference on Signals, System, Computer(ACSSC-2000).2000.1412–1416.
[90] Choi S, Hong H, Glotin H, Berthommier F. Multichannel signal separation for cocktail party speechrecognition:a dynamic recurrent network [J]. Neurocomputing,2002,49(1-4):299–314.
[91] Douglas S C, Sawada H, Makino S. Natural gradient multichannel blind deconvolution and speechseparation using causal FIR filters [J].. IEEE Trans. Speech Audio Processing,2005,13(1):92–104.
[92] Comon P, Jutten C. Handbook of Blind Source Separation: Independent Component Analysis andApplications [M]. Salt Lake City, USA: Academic Press,2010.
[93] Amari S I, Cichocki A, Yang H H. A new learning algorithm for blind signal separation [C]. In:Touretzky T, Mozer M, Hasselmo M, eds. Advances in Neural Information Processing Systems. MITpress,1996.757–763.
[94] Yang H H, Amari S I. Adaptive on-line learning algorithms for blind separation—maximum entropyand minimum mutual information [J]. Neural Computation,1998,9(7):1457–1482.
[95] Hild II K E, Erdogmus D, Príncipe J. Blind source separation using Renyi’s mutual information [J].IEEE Signal Process. Lett.,2001,8(6):174–176.
[96] Luo Z Q, Lu J. On blind source separation using mutual information criterion [J]. MathematicalProgramming,2003,97(3):587–603.
[97] Mokhtari F, Babaie-Zadeh M, Jutten C. Blind separation of bilinear mixtures using mutualinformation minimization [C]. In: Proc. of IEEE International Workshop on Machine Learning forSignal Processing (MLSP2009). New York: IEEE Press,2009.1–6.
[98] Pham D T. Blind separation of instantaneous mixture of sources via the Gaussian mutual informationcriterion [J]. Signal Process.,2001,81(4):855–870.
[99] Pham D T. Mutual information approach to blind separation of stationary sources [J]. IEEE Trans.Information Theory,2002,48(7):1935–1946.
[100] Pham D T. Mutual information approach to blind separation-deconvolution [C]. In: Proc. of13thEuropean Signal Processing Conference (EUSIPCO-2005).2005.684–687.
[101] Rhabi M E, Gelle G, Fenniri H, Delaunay G. A penalized mutual information criterion for blindseparation of convolutive mixtures [J]. Signal Process.,2004,84(10):1979–1984.
[102] Yang H H, Amari S, Cichocki A. Information theoretic approach to blind separation of sources innon-linear mixture [J]. Signal Process.,1998,64(3):291–300.
[103] Taleb A, Jutten C. Source separation in post-nonlinear mixtures [J]. IEEE Trans. Signal Process.,1999,47(10):2807–2820.
[104] Achard S, Pham D T, Jutten C. Criteria based on mutual information minimization for blind sourceseparation in post nonlinear mixtures [J]. Signal Process.,2005,85(5):965–974.
[105] Amari S. Natural gradient works efficiently in learning [J]. Neural Computation,1998,10(2):251–276.
[106] Figueiredo F, Ynoguti C. On the improvement of the learning rate in blind source separation usingtechniques from artificial neural networks theory [C]. In: Proc. of the International Workshop onTelecommunications (IWT-2009). New York: IEEE Press,2009.224–229.
[107] Li H, Shen Y H, Xu K. Neural network with momentum for dynamic source separation and itsconvergence analysis [J]. Journal of Networks,2011,6(5):791–798.
[108] Cichocki A, Amari S, Siwek K, Tanaka T, et al., ICALAB toolboxes [EB/OL].http://www.bsp.brain.riken.go.jp/ICALAB/ICALABSignalProc/benchmarks,2013-12-21.
[109] Jia P, Zhang H Y, Shi X Z. Blind source separation based on non-parametric density estmiation [J].Circ. Syst. Signal Process.,2003,22(1):57–67.
[110] Choi S, Cichocki A, Zhang L L, Amari S. Approximate maximum likelihood source separation usingthe natural gradient [J]. IEICE Trans. Fund. Electron. Comm. Comput. Sci.,2003, E86-A(1):198–205.
[111] Nishimori Y, Akaho S, Plumbley M D. Natural conjugate gradient on complex flag manifolds forcomplex independent subspace [C]. In: K rková V, Neruda R, Koutník J, eds. Proc. of the18thInternational Conference on Artifcial Neural Networks, Lecture Notes in Computer Science(ICANN-2008). Berlin Heidelberg: Springer,2008,5163:165–174.
[112] Edelman A, Arias T A, Smith S T. The geometry of algorithms with orthogonality constraints [J].SIAM J. Matrix Anal.&Appl.,1999,20(2):303–353.
[113] Cichocki A, Karhunen J, Kasprzak W, Vigario R. Neural networks for blind separation with unknownnumber of sources. Neurocmputing,1999,24:55–93.
[114] Choi S, Cichocki A, Amari S. Flexible independent component analysis [J]. J. VLSI Signal Process.Syst. Signal Image Video Technol.,2000,26(1-2):25–38.
[115] Mittal A, Paragios N. Motion-based background subtraction using adaptive kernel density estimation[C]. In: Proc. of the2004IEEE Computer Society Conference on Computer Vision and PatternRecognition (CVPR2004). New York: IEEE Press,2004,2:302–309.
[116] Fiori S. Probability density function learning by unsupervised neurons [J]. Int. J. Neural Syst.,2001,11(5):399–417.
[117] Jones M C, Marron J S, Sheather S J. Progress in data-based bandwidth selection for kernel densityestimation [J]. Comput. Stat.,1996,11:337–381.
[118] Karvanen J, Koivunen V. Blind separation methods based on Pearson system and its extensions [J].Signal Process.,2002,82(4):663–673.
[119] Smith J S. The local mean decomposition and its application to EEG perception data [J]. J. Roy. Soc.Inter.,2005,2(5):443–454.
[120] Wang Y X, He Z J, Xiang J W, Zi Y Y. Application of local mean decomposition to the surveillanceand diagnostics of low-speed helical gearbox [J]. Mech. Mach. Theory,2012,47:62–73.
[121] Yang Y, Cheng J S, Zhang K. An ensemble local means decomposition method and its application tolocal rub-impact fault diagnosis of the rotor systems [J]. Measurement,2012,45(3):561–570.
[122] Peng H, Long F, Ding C. Feature selection based on mutual information: criteria of max-dependency,max-relevance, and min-redundancy [J]. IEEE Trans. Pattern Analysis and Machine Intelligence,2005,27(8):1226–1238.
[123] Zhu J, Tang B, Chen B. An AMUSE-based approach for detection and blind separation ofmulti-component radar signals [C]. In: Proc. of the8th International Conference on ElectronicMeasurement and Instruments (ICEMI-2007),2007.1037–1040.
[124] Teixeira A R, Tomé A M, Lang E W, Stadlthanner K. Delayed AMUSE–a tool for blind sourceseparation and denoising [C]. In: Puntonet C G, Prieto A. eds. Proc. of the5th InternationalConference on Independent Component Analysis and Blind Signal Separation, Lecture Notes inComputer Science (ICABSS-2004). Berlin Heidelberg: Springer,2004,3195:287–294.
[125] Fishler E, Poor H V. Estimation of the Number of Sources in Unbalanced Arrays via InformationTheoretic Criteria [J]. IEEE Trans. Signal Process.,2005,53(9):3543–3553.
[126] Li Y Q, Amari S, Cichocki A, Ho D W C, Xie S L. Underdetermined blind source separation based onsparse representation [J]. IEEE Trans. Signal Process.,2006,54(2):423–437.
[127] Bell A J, Sejnowski T J. An information-maximization approach to blind separation and blinddeconvolution [J]. Neural Computation,1995,7(6):1129–1159.
[128] Lee T. W, Cirolami M, Sejnowski T J. Independent component analysis using an extended algorithmfor mixed subgaussian and supergaussian sources [J]. Neural Computation,1999,11:409–433.
[129] Cardoso J F. Informax and maximum likelihood for source separation [J]. IEEE Signal Process. Lett.,1997,4:112–114.
[130] Yilmaz, Rickard S. Blind separation of speech mixtures via time-frequency masking [J]. IEEETrans. Signal Process.,2004,52(7):1830–1847.
[2] Choi S, Cichocki A, Park H M, Lee S Y. Blind source separation and independent component analysis:A review [J]. Neural Inf. Process.,2005,6(1):1–57.
[3]张发启,张斌,张喜斌.盲信号处理及应用[M].西安：西安电子科技大学出版社,2006.1–30.
[4]杨竹青,李勇,胡德文.独立成分分析方法综述[J].自动化学报,2002,28(5):762–772.
[5] Hyv rinen A, Karhunen J, Oja E. Independent Component Analysis [M]. New York: John Wiley&Sons,2001.
[6] Khaliq A A, Qureshi I M, Shaha J A. Source extraction from functional magnetic resonance imagingdata using ICA based on fourth-order and exponential contrast functions [J]. J. Chin. Inst. Eng.2013,36(6):730–742.
[7] Ye Y, Zhang Z L, Zeng J, Peng L. A fast and adaptive ICA algorithm with its application to fetalelectrocardiogram extraction [J]. Appl. Math. Comput.,2008,205(2):799–806.
[8] Georgiev P, Theis F, Cichocki A. Sparse component analysis and blind source separation ofunderdetermined mixtures [J]. IEEE Trans. Neural Netw.,2005,16(4):992–996.
[9] Li Y Q, Cichocki A, Amari S. Analysis of sparse representation and blind source separation [J]. NeuralComputation,2004,16(6):1193–1234.
[10] Zhang H, Li L, Li W. Independent vector analysis for convolutive blind noncircular source separation[J]. Signal Process.,2012,92(9):2275–2283.
[11] Attias H. Independent factor analysis [J]. Neural Computation,1999,11:803–851.
[12]张俊萍,刘爱伦.基于独立因子分析法的信号盲分离的应用[J].华东理工大学学报(自然科学版),2008,34(3):410–416.
[13] Antoni J. Blind separation of vibration components: principles and demonstrations [J]. Mech. Syst.Signal Process.,2005,19:1166–1180.
[14] Kociński J, Drgas S, Ozimek E. Evaluation of blind source separation for different algorithms basedon second order statistics and different spatial configurations of directional microphones [J]. Appl.Acoust.,2012,73(2):109–116.
[15] Maazouzi F, Bahi Halima. Type-2Fuzzy Gaussian mixture models for singing voice classification incommercial music production [J]. Int. J. Signal Imag. Syst. Engineer.,2013,6(2):111–118.
[16] Wang F, Li H, Li R. Harmonic signals retrieval approach based on blind source separation [J]. Circ.,Syst. Signal Process.,2010,29(4):669–685.
[17]罗一涵,付承毓.基于中频的实时图像盲复原算法[J].四川大学学报(工程科学版),2010,42(6):109–118.
[18] Naceur M, Loghmari M, Boussema M. The contribution of the sources separation method in thedecomposition of mixed pixels [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(2):2642–2653.
[19] Kolba J, Jouny I. Blind source separation in tumor detection in mammograms [C]. In: Proc. of theIEEE32nd Annual Northeast Bioengineering Conference. New York: IEEE Press,2006.65–66.
[20] Congedo M, Pailler C G, Jutten C. On the blind source separation of human electroencephalogram byapproximate joint diagonalization of second order statistic [J]. Clinical Neurophysiology,2008,199(12):2677–2686.
[21] Guo X, Chang C, Lam Y. Blind separation of electron paramagnetic resonance signals using diversityminimization [J]. J. Magn. Reson.,2010,204(1):26–36.
[22] Sun Y, Ridge C, Rio F, Shaka A J, Xin J. Postprocessing and sparse blind source separation of positiveand partially overlapped data [J]. Signal Process.,2011,91(8):1838–1851.
[23] Pauca V P, Shahnaz F, Berry W, Plemmons R J. Text mining using nonnegative matrix factorizations[C]. In: Proc. of the4th SIAM International Conference on Data Mining (ICDM-2004),2004.452–456.
[24]张安清,邱天爽.波束域的信号盲分离方法[J].系统工程与电子技术,2008,30(9):1628–1631.
[25] Budipriyanto A. Blind source separation based dynamic parameter identification of a multi-storymoment-resisting frame building under seismic ground motions [J]. Procedia Engineer.,2013,54:299–307.
[26] Lathauwer L D, Castaing J. Tensor-based techniques for the blind separation of DS-CDMA signals [J].Signal Process.,2007,87(2):322–336.
[27]杨祖元.盲信号分离算法分析应用研究[D].[博士学位论文].广州:华南理工大学电子与信息学院,2009.
[28] Jutten C, Herault J. Blind separation of source part I: an adaptive algorithm based on neuromimeticarchitecture [J]. Signal Process.,1991,24:1–10.
[29] Comon P. Independent component analysis, a new concept?[J]. Signal Process.,1994,36:287–314.
[30] Cao X R, Liu R. General approach to blind source separation [J]. IEEE Trans. Signal Process.,1996,44(3):562–571.
[31] Hyv rinen A. The FastICA MATLAB package [EB/OL]. http://www.cis.hut.fi/projects/ica/fastica,2013-12-21.
[32] Novey M, Adali T. On extending the complex FastICA algorithm to noncircular sources [J]．IEEETrans. Signal Process.,2008,56(5):2148–2154.
[33] Zarzoso V, Comon P. Robust Independent component analysis by iterative maximization of thekurtosis contrast with algebraic optimal step size [J]. IEEE Trans. Neural Netw.,2010,21(2):248–261.
[34] Wang Y, Y lmaz, Zhou Z. Phase aliasing correction for robust blind source separation using DUET[J]. Appl. Comput. Harmonic Anal.,2013,35(2):341–349.
[35] Cardoso J F, Souloumiac A. Jacobi angles for simultaneous diagonalization [J]. SIAM J. Matrix Anal.Appl.,1996,17(1):161–164.
[36] Belouchrani A, Abed-Meraim K, Cardoso J F. A blind source separation technique using second-orderstatistics [J]. IEEE Trans. Signal Process.,1997,45(2):434–444.
[37] Joho M, Mathis H. Joint diagonalization of correlation matrices by using gradient methods withapplication to blind signal separation [C]. In: Proc. of IEEE Sensor Array and Multichannel SignalProcessing Workshop. New York: IEEE Press,2002.273–277.
[38] Moreau E. A generalization of joint diagonalization criteria for source separation [J]. IEEE Trans.Signal Process.,2001,49(3):530–541.
[39] Pham D.T. Joint approximate diagonalization of positive definite Hermitian matrices [J]. SIAM J.Matrix Anal. Appl.,2001,22(4):1136–1152.
[40] Van Der Veen A J. Joint diagonalization via subspace fitting techniques [C]. In: Proc. of IEEEInternational Conference on Acoustics, Speech, and Signal Processing (ICASSP-2001). New York:IEEE Press,2001.2773–2776.
[41] Souloumiac A. Nonorthogonal joint diagonalization by combining givens and hyperbolic rotations [J].IEEE Trans. Signal Process.,2009,57(6):2222–2231.
[42]张华,冯大政,聂卫科,徐先峰.非正交联合对角化盲源分离算法[J].西安电子科技大学学报(自然科学版),2008,35(1):27–31.
[43]李昌利,曹嘉毅.基于循环优化的矩阵联合对角化算法及在盲源分离中的应用[J].四川大学学报（工程科学版）,2011,43(5):159–162.
[44] Ye J M, Jin H H, Lou S T, You K J. An optimized EASI algorithm [J]. Signal Process.,2009,89(3):333–338.
[45] Liu D, Liu X. Informax algorithm based on linear ICA neural network for BSS problems [C]. In: Proc.of the4th World Congress on Intelligent Control and Automation (WCICA-2002),2002.1949–1952.
[46] Zhu X L, Zhang X D, Ding Z Z, Jia Y. Adaptive nonlinear PCA algorithms for blind source separationwithout prewhitening [J]. IEEE Trans. Circ. Syst.,2006,53(3):745–753.
[47]欧世峰,赵晓晖,高颖.结合辅助分离系统的变步长盲源分离算法[J].电子学报,2009,37(7):1588–1593.
[48]付卫红,杨小牛,刘乃安,曾兴雯.基于步长最优化的EASI盲源分离算法[J].四川大学学报(工程科学版),2008,40(1):118–121.
[49] Joho M, Mathis H, Lambert R H. Overdetermined blind source separation: using more sensors thansource signals in a noisy mixture [C]. In: Proc. of Independent Component Analysis and Blind SignalSeparation (ICA-2000).2000.81–86.
[50] Nishikawa T, Abe H, Saruwatari H, Shikano K. Overdetermined blind source separation of realacoustic sounds based on multistage ica using subarray processing [C]. In: Proc. of the3rdIEEEInternational Symposium on Signal Processing and Information Technology (ISSPIT-2003). NewYork: IEEE Press,2003.510–513.
[51] Amari S I. Natural gradient learning for over-and under-complete bases in ICA [J]. NeuralCornputation,1999,11(8):1875–1883.
[52] Zhang L Q, Cichocki A, Amari S I. Natural gradient algorithm for blind separation of overdeterminedmixture with additive noise [J]. IEEE Signal Process. Lett.,1999,6(11):293–295.
[53] Omlor L, Giese M A. Blind source separation for over-determined delayed mixtures [J]. Advances inNeural Information Processing Systems,2007,19:1074–1081.
[54] Duarte L T, Suyama R, Attux R, Deville Y, Romano J M T, Jutten C. Blind source separation ofoverdetermined linear-quadratic mixtures [C]. In: Vigneron V, Zarzoso V, Moreau E, Gribonval R,Vincent E.(eds.) Proc. of the9thInternational Conference on Latent Variable Analysis and SignalSeparation (LVA/ICA-2010). Berlin: Springer Berlin Heidelberg,6365:263–270.
[55] Lathauwer L D, Castaing J, Cardoso J F. Fourth-order cumulant-based blind identification ofunderdetermined mixtures [J]. IEEE Trans. Signal Process.,2007,55(6):2965–2973.
[56] Thomas J, Deville Y, Shahram H. Differential fast fixed-point algorithm for underdeterminedinstantaneous and convolutive partial blind source separation [J]. IEEE Trans. Signal Process.,2007,55(7):3717–3729.
[57] Bofill P, Zibulevsky M. Underdetermined blind source separation using sparse representations [J].Signal Process.,2001,81(11):2353–2362.
[58] Sadhu A, Hazra B, Narasimhan S. Decentralized modal identification of structures using parallelfactor decomposition and sparse blind source separation [J]. Mech. Syst. Signal Process.,2013,41(1-2):396–419.
[59] Lewicki M S, Sejnowski T J, Hughes H. Learning overcomplete representations [J]. NeuralComputation,2000,12:337–365.
[60] Zibulevsky M, Pearlmutter B A. Blind source separation by sparse decomposition in a signaldictionary [J]. Neural Computation,2001,13(4):863–882.
[61] Theis F J, Puntonet C G, Lang E W. Median-based clustering for underdetermined blind signalprocessing [J]. IEEE Signal Process. Lett.,2006,13(2):96–99.
[62] Thiagarajan J J, Ramamurthy K N, Spanias A. Mixing matrix estimation using discriminativeclustering for blind source separation [J]. Digital Signal Process.,2013,23(1):9–18.
[63] Linh-Trung N, Belouchrani A, Abed-Meraim K, Boashash B. Separating more sources than sensorsusing time-frequency distributions [J]. EURASIP J. Applied Signal Process.,2005,2005(17):2828–2847.
[64] Theis F., Lang E W, Puntonet C G. A geometric algorithm for overcomplete linear ICA [J].Neurocomputing,2004,56:381–398.
[65] Peng D, Xiang Y. Underdetermined blind separation of non-sparse sources using spatialtime-frequency distributions [J]. Digital Signal Process.,2010,20(2):581–596.
[66] Deville Y, Benali M, Abrard F. Differential source separation for underdetermined instantaneous orconvolutive mixtures: concept and algorithms [J]. Signal Process.,2004,84(10):1759–1776.
[67] Shi Z, Zhang C. Nonlinear innovation to blind source separation [J]. Neurocomputing,2007,71(1-3):406–410.
[68] Lin J K, Grier D G, Cowan J D. Source separation and density estimation by faithful equivariant SOM[C]. In: Proc. of Advances in Neural Information Processing Systems9(ANIPS-1997), MA: MITPress,1997.536–542.
[69] Almeida L B. MISEP-linear and nonlinear ICA based on mutual information [J]. J. Mach. Learn. Res.,2003,4:1297–1318.
[70] Almeida L B. Linear and nonlinear ICA based on mutual information-the MISEP method [J]. SignalProcess.,2004,84(2):231–245.
[71] Martinez D, Bray A. Nonlinear blind separation using kernels [J]. IEEE Trans. Nueral Netw.,2003,14(l):228–235.
[72] Solazzi M, Piazza F, Uneini A. Nonlinear blind source separation by spline neural networks [C]. In:Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-2001).New York: IEEE Press,2001,5:2781–2784.
[73] Milani F, Solazzi M, Uneini A. Blind source separation of convolutive nonlinear mixtures by flexiblespline nonlinear functions [C]. In: Proc. of IEEE International Conference on Acoustics, Speech, andSignal Processing (ICASSP-2002). New York: IEEE Press,2002,2:1641–1644.
[74] Honkela A, Valpola H, Ilin A, Karhunen J. Blind separation of nonlinear mixtures by variationalBayesian learning,Digital Signal Processing [J].2007,17(5):914–934.
[75] Song K, Ding M, Wang Q, Liu W. Blind source separation in post-nonlinear mixtures using naturalgradient descent and particle swarm optimization algorithm [C]. In: Proc. of Advances in NeuralNetworks, Lecture Notes in Computer Science (ISNN-2007),2007,4493:721–730.
[76]陶涛,黄高明,赵治华.后非线性混叠信号盲源分离算法综述[J].控制与决策,2010,25(8):1121–1128.
[77] Tan Y, Wang J, Zurada J. Nonlinear blind source separation using a radial basis function network [J].IEEE Trans. Neural Netw.,2001,12(1):124–134.
[78] Hosseini S, Deville Y. Recurrent networks for separating extractable-target nonlinear mixtures. Part II:blind configurations [J]. Signal Process.,2013,93(4):671–683.
[79] Deville Y, Hosseini S. Recurrent networks for separating extractable-target nonlinear mixtures. Part I:non-blind configurations [J]. Signal Process.,2009,89(4):378–393.
[80]楼红伟,胡光锐.基于小波域的非平稳卷积混合语音信号的自适应盲分离[J].控制与决策,2004,19(1):73–76.
[81] Dam H H, Cantoni A, Nordholm S, et al. Second order blind signal separation for convolutivemixtures using conjugate gradient [J]. IEEE Signal Process. Lett.,2008,15:79–82.
[82] Araki S, Mukai R, Makino S. The fundamental limitation of frequency domain blind sourceseparation for convolutive mixtures of speech [J]. IEEE Trans. Speech Audio Process.,2003,11(2):109–116.
[83] Parra L, Spence C. Convolutive blind separation of nonstationary sources [J]. IEEE Trans. SpeechAudio Process.,2000,8(3):320–327.
[84] Saruwatari H, Kawamura T, Nishikawa T, Lee A, Shikano K. Blind source separation based on afast-convergence algorithm combining ICA and beamforming [J]. IEEE Trans. Speech Audio Process.,2006,14(2):666–678.
[85] Murata N, Ikeda S, Ziehe A. An approach to blind source separation based on temporal structure ofspeech signals [J]. Neurocomputing,2001,41:1–24.
[86] Kawamoto M, Matsucka K, Ohnishi N. A method of blind separation for convolved non-stationarysignals [J]. Neurocomputing,1998,22(1-3):157–171.
[87] Bousbia S H, Belouchrani A, Abed M K. Blind separation of convolutive mixtures using joint blockdiagonalization [C]. In: Proc. of IEEE International Symposium on Signal Processing and itsApplications (ISSPA-2001). New York: IEEE Press,2001.13–16.
[88] Yellin D, Weinstein E. Multichannel signal separation: methods and analysis [J]. IEEE Trans. SignalProcess.,1996,44(1):106–118.
[89] Sun X, Douglas S C. Multichannel blind deconvolution of arbitrary signals: adaptive algorithms andstability analysis [C]. In: Proc. of the34thAsilomar Conference on Signals, System, Computer(ACSSC-2000).2000.1412–1416.
[90] Choi S, Hong H, Glotin H, Berthommier F. Multichannel signal separation for cocktail party speechrecognition:a dynamic recurrent network [J]. Neurocomputing,2002,49(1-4):299–314.
[91] Douglas S C, Sawada H, Makino S. Natural gradient multichannel blind deconvolution and speechseparation using causal FIR filters [J].. IEEE Trans. Speech Audio Processing,2005,13(1):92–104.
[92] Comon P, Jutten C. Handbook of Blind Source Separation: Independent Component Analysis andApplications [M]. Salt Lake City, USA: Academic Press,2010.
[93] Amari S I, Cichocki A, Yang H H. A new learning algorithm for blind signal separation [C]. In:Touretzky T, Mozer M, Hasselmo M, eds. Advances in Neural Information Processing Systems. MITpress,1996.757–763.
[94] Yang H H, Amari S I. Adaptive on-line learning algorithms for blind separation—maximum entropyand minimum mutual information [J]. Neural Computation,1998,9(7):1457–1482.
[95] Hild II K E, Erdogmus D, Príncipe J. Blind source separation using Renyi’s mutual information [J].IEEE Signal Process. Lett.,2001,8(6):174–176.
[96] Luo Z Q, Lu J. On blind source separation using mutual information criterion [J]. MathematicalProgramming,2003,97(3):587–603.
[97] Mokhtari F, Babaie-Zadeh M, Jutten C. Blind separation of bilinear mixtures using mutualinformation minimization [C]. In: Proc. of IEEE International Workshop on Machine Learning forSignal Processing (MLSP2009). New York: IEEE Press,2009.1–6.
[98] Pham D T. Blind separation of instantaneous mixture of sources via the Gaussian mutual informationcriterion [J]. Signal Process.,2001,81(4):855–870.
[99] Pham D T. Mutual information approach to blind separation of stationary sources [J]. IEEE Trans.Information Theory,2002,48(7):1935–1946.
[100] Pham D T. Mutual information approach to blind separation-deconvolution [C]. In: Proc. of13thEuropean Signal Processing Conference (EUSIPCO-2005).2005.684–687.
[101] Rhabi M E, Gelle G, Fenniri H, Delaunay G. A penalized mutual information criterion for blindseparation of convolutive mixtures [J]. Signal Process.,2004,84(10):1979–1984.
[102] Yang H H, Amari S, Cichocki A. Information theoretic approach to blind separation of sources innon-linear mixture [J]. Signal Process.,1998,64(3):291–300.
[103] Taleb A, Jutten C. Source separation in post-nonlinear mixtures [J]. IEEE Trans. Signal Process.,1999,47(10):2807–2820.
[104] Achard S, Pham D T, Jutten C. Criteria based on mutual information minimization for blind sourceseparation in post nonlinear mixtures [J]. Signal Process.,2005,85(5):965–974.
[105] Amari S. Natural gradient works efficiently in learning [J]. Neural Computation,1998,10(2):251–276.
[106] Figueiredo F, Ynoguti C. On the improvement of the learning rate in blind source separation usingtechniques from artificial neural networks theory [C]. In: Proc. of the International Workshop onTelecommunications (IWT-2009). New York: IEEE Press,2009.224–229.
[107] Li H, Shen Y H, Xu K. Neural network with momentum for dynamic source separation and itsconvergence analysis [J]. Journal of Networks,2011,6(5):791–798.
[108] Cichocki A, Amari S, Siwek K, Tanaka T, et al., ICALAB toolboxes [EB/OL].http://www.bsp.brain.riken.go.jp/ICALAB/ICALABSignalProc/benchmarks,2013-12-21.
[109] Jia P, Zhang H Y, Shi X Z. Blind source separation based on non-parametric density estmiation [J].Circ. Syst. Signal Process.,2003,22(1):57–67.
[110] Choi S, Cichocki A, Zhang L L, Amari S. Approximate maximum likelihood source separation usingthe natural gradient [J]. IEICE Trans. Fund. Electron. Comm. Comput. Sci.,2003, E86-A(1):198–205.
[111] Nishimori Y, Akaho S, Plumbley M D. Natural conjugate gradient on complex flag manifolds forcomplex independent subspace [C]. In: K rková V, Neruda R, Koutník J, eds. Proc. of the18thInternational Conference on Artifcial Neural Networks, Lecture Notes in Computer Science(ICANN-2008). Berlin Heidelberg: Springer,2008,5163:165–174.
[112] Edelman A, Arias T A, Smith S T. The geometry of algorithms with orthogonality constraints [J].SIAM J. Matrix Anal.&Appl.,1999,20(2):303–353.
[113] Cichocki A, Karhunen J, Kasprzak W, Vigario R. Neural networks for blind separation with unknownnumber of sources. Neurocmputing,1999,24:55–93.
[114] Choi S, Cichocki A, Amari S. Flexible independent component analysis [J]. J. VLSI Signal Process.Syst. Signal Image Video Technol.,2000,26(1-2):25–38.
[115] Mittal A, Paragios N. Motion-based background subtraction using adaptive kernel density estimation[C]. In: Proc. of the2004IEEE Computer Society Conference on Computer Vision and PatternRecognition (CVPR2004). New York: IEEE Press,2004,2:302–309.
[116] Fiori S. Probability density function learning by unsupervised neurons [J]. Int. J. Neural Syst.,2001,11(5):399–417.
[117] Jones M C, Marron J S, Sheather S J. Progress in data-based bandwidth selection for kernel densityestimation [J]. Comput. Stat.,1996,11:337–381.
[118] Karvanen J, Koivunen V. Blind separation methods based on Pearson system and its extensions [J].Signal Process.,2002,82(4):663–673.
[119] Smith J S. The local mean decomposition and its application to EEG perception data [J]. J. Roy. Soc.Inter.,2005,2(5):443–454.
[120] Wang Y X, He Z J, Xiang J W, Zi Y Y. Application of local mean decomposition to the surveillanceand diagnostics of low-speed helical gearbox [J]. Mech. Mach. Theory,2012,47:62–73.
[121] Yang Y, Cheng J S, Zhang K. An ensemble local means decomposition method and its application tolocal rub-impact fault diagnosis of the rotor systems [J]. Measurement,2012,45(3):561–570.
[122] Peng H, Long F, Ding C. Feature selection based on mutual information: criteria of max-dependency,max-relevance, and min-redundancy [J]. IEEE Trans. Pattern Analysis and Machine Intelligence,2005,27(8):1226–1238.
[123] Zhu J, Tang B, Chen B. An AMUSE-based approach for detection and blind separation ofmulti-component radar signals [C]. In: Proc. of the8th International Conference on ElectronicMeasurement and Instruments (ICEMI-2007),2007.1037–1040.
[124] Teixeira A R, Tomé A M, Lang E W, Stadlthanner K. Delayed AMUSE–a tool for blind sourceseparation and denoising [C]. In: Puntonet C G, Prieto A. eds. Proc. of the5th InternationalConference on Independent Component Analysis and Blind Signal Separation, Lecture Notes inComputer Science (ICABSS-2004). Berlin Heidelberg: Springer,2004,3195:287–294.
[125] Fishler E, Poor H V. Estimation of the Number of Sources in Unbalanced Arrays via InformationTheoretic Criteria [J]. IEEE Trans. Signal Process.,2005,53(9):3543–3553.
[126] Li Y Q, Amari S, Cichocki A, Ho D W C, Xie S L. Underdetermined blind source separation based onsparse representation [J]. IEEE Trans. Signal Process.,2006,54(2):423–437.
[127] Bell A J, Sejnowski T J. An information-maximization approach to blind separation and blinddeconvolution [J]. Neural Computation,1995,7(6):1129–1159.
[128] Lee T. W, Cirolami M, Sejnowski T J. Independent component analysis using an extended algorithmfor mixed subgaussian and supergaussian sources [J]. Neural Computation,1999,11:409–433.
[129] Cardoso J F. Informax and maximum likelihood for source separation [J]. IEEE Signal Process. Lett.,1997,4:112–114.
[130] Yilmaz, Rickard S. Blind separation of speech mixtures via time-frequency masking [J]. IEEETrans. Signal Process.,2004,52(7):1830–1847.