基于稀疏表示的语音信号欠定盲分离技术研究
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摘要
信号处理在各个领域一直有着重要的地位,而伴随着移动通信和地质勘探技术的发展,迫切需要一种新的信号处理方法,盲信号处理就应运而生。盲源分离是二十世纪九十年代发展起来的一种新兴信号处理方法,它在研究语音增强、图像识别、生物工程信号、通信信号以及地震探测等领域中有非常重要的理论价值。
传统盲源分离往往假设传感器个数大于信源数目,但是伴随着盲源分离问题的深入研究,欠定盲源分离问题备受关注,因为它是更符合实际,也是更具挑战的。在此条件下系统是不可逆的,传统的盲源分离算法失效,所以本文在语音信号稀疏表示的基础上,对语音信号欠定盲源分离的关键技术进行了研究。
本文首先介绍盲源分离的发展现状,并对传统盲源分离算法进行了阐述。然后对欠定盲源分离的理论基础及关键技术进行了探索性研究。其中“两步法”是欠定盲源分离问题的热点,即首先通过聚类算法估计出混合矩阵,然后通过优化算法得到源信号估计,它与信号稀疏表示以及过完备基的选择有着密切关系。本文主要研究的内容如下：
在信号稀疏表示的基础上,本文将目前模式识别聚类理论中最为成熟的模糊C均值聚类算法,运用到混合矩阵估计中。它克服了传统用势函数估计混合矩阵的方法中存在的参数选择复杂,势函数定义缺乏理论指导等缺点。但是模糊聚类自身存在对初始值敏感,易陷入局部最优等缺点,因此将其与差分进化结合,提出DE-FCM的混合矩阵估计算法,实现无监督聚类,参数选择简单,收敛速度快,估计准确等优点,并且达到全局优化。
得到混合矩阵的估计之后,为了估计出不同稀疏程度的源信号,本文将平滑l0范数思想引入源信号估计中,不再使用最小l1范数的方法。因为最小化l1范数只有在信号足够稀疏时,才可以很好的恢复出源信号。而平滑l0范数直接利用一个近似函数来逼近l0范数以保证估计的性能,并利用一个控制因子来决定估计出的源信号稀疏性强度。实验表明该方法可以很好的实现源信号估计,而且得到源信号估计更符合混合模型。
Signal processing plays an important role in various fields and with the development of mobile communication and the geological prospecting technology, a new kind of signal processing is in an urgent need, then blind signal processing arises at the historic moment. Blind source separation is developed as a new kind of signal processing method 1990s, which has important theoretical value in researching the speech enhancement, the image recognition, the bioengineering signal, communication signals, and seismic exploration.
Traditional blind source separation is always based on the assumption that the sensor number is more than source number, but with the further research of blind source separation more attention has been paid to underdetermined blind source separation which is more conform to the fact and would be more challenging. In this condition the system is irreversible, so the traditional blind source separation algorithm would fail. In this paper, based on sparse representation of speech signal, the key technologies of underdetermined blind source separation are explained.
In this paper, the development status of blind source separation is briefly introduced firstly. Then explorative study is made on theoretical basis and key technology of the underdetermined blind source separation. the basic algorithms are also discussed. "Two-step" algorithm cluster-then-optimization to estimate the mixing matrix and source signals separately is a hotspot of underdetermined blind source separation, and it has close relation with signal sparse representation and overcomplete basis. This paper mainly studies the content as follows:
Based on the sparse representation of signals, the fuzzy C-means clustering algorithm whose theoretical basis is most mature among pattern recognition clustering theory is applied to estimate the mixing matrix here. It can overcome the disadvantage of traditional potential function algorithm used to estimate the mixing matrix, such as complexity in the parameter selection and lack of theoretical guidance to define the potential function. But fuzzy C-means clustering is sensitive to the initial value and easy to be trapped in local optimum, so it will be combined with the differential evolution, named DE-FCM algorithm to realize unsupervised clustering, simple parameter selection, fast convergence rate, more accurate estimation and achieve global optimization finally.
After getting the mixing matrix estimation, in order to estimate source signals with different degree of sparsity, this paper proposed a method based on the smoothed l0 norm to recover the source signals. Here minimum norm l1 method is no longer used, because minimize l1 norm can get a good result only when the signals are sparse enough. The method based on the smoothed l0 only uses an approximate function to approximate l0 norm directly and the quality of the approximation depends on a parameter called control factor. Experiments show that this method can get good result and the result can fit the mixing model better.
传统盲源分离往往假设传感器个数大于信源数目,但是伴随着盲源分离问题的深入研究,欠定盲源分离问题备受关注,因为它是更符合实际,也是更具挑战的。在此条件下系统是不可逆的,传统的盲源分离算法失效,所以本文在语音信号稀疏表示的基础上,对语音信号欠定盲源分离的关键技术进行了研究。
本文首先介绍盲源分离的发展现状,并对传统盲源分离算法进行了阐述。然后对欠定盲源分离的理论基础及关键技术进行了探索性研究。其中“两步法”是欠定盲源分离问题的热点,即首先通过聚类算法估计出混合矩阵,然后通过优化算法得到源信号估计,它与信号稀疏表示以及过完备基的选择有着密切关系。本文主要研究的内容如下：
在信号稀疏表示的基础上,本文将目前模式识别聚类理论中最为成熟的模糊C均值聚类算法,运用到混合矩阵估计中。它克服了传统用势函数估计混合矩阵的方法中存在的参数选择复杂,势函数定义缺乏理论指导等缺点。但是模糊聚类自身存在对初始值敏感,易陷入局部最优等缺点,因此将其与差分进化结合,提出DE-FCM的混合矩阵估计算法,实现无监督聚类,参数选择简单,收敛速度快,估计准确等优点,并且达到全局优化。
得到混合矩阵的估计之后,为了估计出不同稀疏程度的源信号,本文将平滑l0范数思想引入源信号估计中,不再使用最小l1范数的方法。因为最小化l1范数只有在信号足够稀疏时,才可以很好的恢复出源信号。而平滑l0范数直接利用一个近似函数来逼近l0范数以保证估计的性能,并利用一个控制因子来决定估计出的源信号稀疏性强度。实验表明该方法可以很好的实现源信号估计,而且得到源信号估计更符合混合模型。
Signal processing plays an important role in various fields and with the development of mobile communication and the geological prospecting technology, a new kind of signal processing is in an urgent need, then blind signal processing arises at the historic moment. Blind source separation is developed as a new kind of signal processing method 1990s, which has important theoretical value in researching the speech enhancement, the image recognition, the bioengineering signal, communication signals, and seismic exploration.
Traditional blind source separation is always based on the assumption that the sensor number is more than source number, but with the further research of blind source separation more attention has been paid to underdetermined blind source separation which is more conform to the fact and would be more challenging. In this condition the system is irreversible, so the traditional blind source separation algorithm would fail. In this paper, based on sparse representation of speech signal, the key technologies of underdetermined blind source separation are explained.
In this paper, the development status of blind source separation is briefly introduced firstly. Then explorative study is made on theoretical basis and key technology of the underdetermined blind source separation. the basic algorithms are also discussed. "Two-step" algorithm cluster-then-optimization to estimate the mixing matrix and source signals separately is a hotspot of underdetermined blind source separation, and it has close relation with signal sparse representation and overcomplete basis. This paper mainly studies the content as follows:
Based on the sparse representation of signals, the fuzzy C-means clustering algorithm whose theoretical basis is most mature among pattern recognition clustering theory is applied to estimate the mixing matrix here. It can overcome the disadvantage of traditional potential function algorithm used to estimate the mixing matrix, such as complexity in the parameter selection and lack of theoretical guidance to define the potential function. But fuzzy C-means clustering is sensitive to the initial value and easy to be trapped in local optimum, so it will be combined with the differential evolution, named DE-FCM algorithm to realize unsupervised clustering, simple parameter selection, fast convergence rate, more accurate estimation and achieve global optimization finally.
After getting the mixing matrix estimation, in order to estimate source signals with different degree of sparsity, this paper proposed a method based on the smoothed l0 norm to recover the source signals. Here minimum norm l1 method is no longer used, because minimize l1 norm can get a good result only when the signals are sparse enough. The method based on the smoothed l0 only uses an approximate function to approximate l0 norm directly and the quality of the approximation depends on a parameter called control factor. Experiments show that this method can get good result and the result can fit the mixing model better.
引文
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[25]M.S. Lewicki and T.J. Sejnowski. Learning overcomplete representations[J]. Neural Comput.,12(2), pp.337-365,2000.
[26]M. Zibulevsky and B.A. Pearlmutter. Blind Source Separation by Sparse Decompo-sition[J]. Neural Comput.,13(4), pp.863-882,2001.
[27]A. Jourjine, Scott Rickard and O. Yilmaz. Blind separation of disjoint orthogonal siagnals:Demixing N sources from 2 mixtures[J]. IEEE Int. Conf. Acoustics, Speech Signal Processing, vol.5, Istanbul, Turkey, pp.2985-2988,2000.
[28]Mariko Aoki, et al.. Sound source segregation based on estimating incident angle of each frequency component of input signals acquired by multiple microphones [J]. Acou. Sci.&Tech.22, pp.149-157,2001.
[29]Frederic Abrard and Yannick Deville. Blind separation of dependent sources using time-frequency ratio of mixtures approach[J]. Signal Processing of Applications, Paris, France, Jul.1-4,2003.
[30]Frederic Abrard and Yannick Deville. A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources[J]. Signal Process, vol.85, no.7, pp.1389-1403, Jul.2005.
[31]P. Bofill and M. Zibulevsky. Underdetermined blind source separation using sparse representations[J]. Signal Process,81(11), pp.2353-362,2001.
[32]王建英,尹忠科,张春梅.信号与图像的稀疏分解及初步应用[M].成都：西南交通大学出版社,2004：49-60.
[33]Arthur P.L. and Philipos C.L.. Voiced/unvoiced speech discrimination in noise using Gabor atomic decomposition[J]. Pmc of IEEE ICASSP,1(4), pp.820-828,2003, HongKong.
[34]David G Avellaneda M. and Mallat S.. Adaptive greedy approximation. Constr. Approx., 13(1), pp.57-98,1997.
[35]Candes E. and Donoho D.. New tight frames of curvelets and optimal representations of objects with C2 singularities[J]. Tech. rep., Standford University,2002,37.
[36]Ronald R. Coifman and Mladen V. Wickerhauser. Entropy-based algorithms for best basis selection[J]. IEEE Trans. Information Theory,38(2), pp.713-718, Mar.1992.
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[40]Yuanqing Li, Shun-ichi Amari and A. Cichocki. Analysis of sparse representation and blind source separation[J]. Neural Computation 16, pp.1193-1234,2004.
[41]Yuanqing Li, et al.. Underdetermined blind source separation based on sparse represent-tation[J]. IEEE Trans. Sig. Pro.,54(2) Feb.2006.
[42]Qi Lv and Xianda Zhang. A unified method for blind separation of sparse sources with unknown source number[J]. IEEE signal processing letters,13(1), pp.49-51, Jan. 2006.
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[2]S. Amari and A. Cichocki. Adaptive blind signal processing-neural network approaches[J]. Proceedings IEEE,86:1186-1187,1998.
[3]James V. Stone. Independent Component Analysis. A Tutorial Introduction[M]. The MIT Press, Cambrige, Massachusetts, London, England, pp5-10,2004.
[4]Andrzej Cichocki, Shun-ichi Amari.自适应盲信号与图像处理自适应盲信号与图像处理[M].北京：电子工业出版社,2005：12-46,99-108.
[5]马建仓,牛奕龙,陈海洋.盲信号处理[M].北京：国防工业出版社,2006：2-9.
[6]J. Herault, et al.. Space or time adaptive signal processing by neural network models, In Denker ed.:neural network for computing[J]. AIP Conference Proceedings,151,1986, American Institute of Physics.
[7]C. Jutten, et al.. Blind separation of sources, Pt. I:An adaptive algorithm based on neuromimetic architecture[J]. Signal processing,24(1), pp.1-10,1991.
[8]P. Comon, et al.. Blind separation of sources, Pt. II:Problem statement [J]. Signal processing,24(1), pp.11-20,1991.
[9]L. Tong, R. Liu, V. Soon and Y.F. Huang. The Indeterminacy and Identifiability of Blind Identification[J]. IEEE Transactions on Circuits and Systems, vol.CAS-21, no.5, pp. 499-509, May 1991.
[10]Common P. Independent component analysis. A new concept?[J]. Signal Processing, 36(3), pp.287-314,1994.
[11]A.J. Bell and T.J. Sejnowski. An information-maximization approach to blind separation and blind deconvolution[J]. Neural Computation 7, pp.1129-1159,1995.
[12]S. Amari. New learing in structural parameter space-natural Riemannian gradient[J]. Advances in Neural Information Processing System,9:127-133,1997.
[13]S. Amari. Natural gradient works efficiently in learing[J]. Neural Computation,10(2), pp.251-276,1998.
[14]A. Hyvarinen, et al.. A fast fixed-point algorithm for independent component analysis[J]. Neural Network, pp.1483-1492,1997.
[15]A. Hyvarinen. Fast and robust fixed-point algorithm for independent component analysis[J]. Neural Computation,11(1), pp.157-193,1999.
[16]T.W. Lee, et al.. Independent component analysis using an extended infomax algorithm for sub-Gaussian and super-Gaussian sources. Neural Computation, 11(2):409-433, 1999.
[17]张贤达.时间序列分析一高阶统计量方法[M].北京：清华大学出版社,1996：20-24.
[18]Yu Xiao, Hu guangrui, Chen wei. Speech enhancement based on second order architecture and information maximization theory[J]. Journal of Shanghai Jiaotong University, vol.E-3, no.2, pp.56-60,1998.
[19]冯大政,史维祥.一种自适应信号盲分离和盲辨识的有效算法[J].西安交通大学学报,1998,32(3)：76-79.
[20]汪军,何政亚.瞬时混叠信号盲分离[J].电子学报,1997,25(4)：1-5.
[21]I.F. Gorodnisky and B.D. Rao. Sparse signal reconstruction from limited data using FOCUSS:A re-weighted minimum norm algorithm[J]. IEEE Trans. Sig. Proc.,45(3), pp.600-616, March 1997.
[22]B.D. Rao. Analysis and Extensions of the FOCUSS algorithm[J]. Journal of IEEE, 1997.
[23]B.D. Rao and K. Kreutz-Delgado. An affine scaling methodology for best basis selection[J]. IEEE trans. sig. proc.,47(1), pp.187-200, January 1999.
[24]T.W. Lee, M. Lewieki, M. Girolami and T.J. Sejnowski. Blind source separation of more sources than mixtures using overcomplete representations[J]. IEEE Signal Proeess Letters,6(4), pp.87-90,1999.
[25]M.S. Lewicki and T.J. Sejnowski. Learning overcomplete representations[J]. Neural Comput.,12(2), pp.337-365,2000.
[26]M. Zibulevsky and B.A. Pearlmutter. Blind Source Separation by Sparse Decompo-sition[J]. Neural Comput.,13(4), pp.863-882,2001.
[27]A. Jourjine, Scott Rickard and O. Yilmaz. Blind separation of disjoint orthogonal siagnals:Demixing N sources from 2 mixtures[J]. IEEE Int. Conf. Acoustics, Speech Signal Processing, vol.5, Istanbul, Turkey, pp.2985-2988,2000.
[28]Mariko Aoki, et al.. Sound source segregation based on estimating incident angle of each frequency component of input signals acquired by multiple microphones [J]. Acou. Sci.&Tech.22, pp.149-157,2001.
[29]Frederic Abrard and Yannick Deville. Blind separation of dependent sources using time-frequency ratio of mixtures approach[J]. Signal Processing of Applications, Paris, France, Jul.1-4,2003.
[30]Frederic Abrard and Yannick Deville. A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources[J]. Signal Process, vol.85, no.7, pp.1389-1403, Jul.2005.
[31]P. Bofill and M. Zibulevsky. Underdetermined blind source separation using sparse representations[J]. Signal Process,81(11), pp.2353-362,2001.
[32]王建英,尹忠科,张春梅.信号与图像的稀疏分解及初步应用[M].成都：西南交通大学出版社,2004：49-60.
[33]Arthur P.L. and Philipos C.L.. Voiced/unvoiced speech discrimination in noise using Gabor atomic decomposition[J]. Pmc of IEEE ICASSP,1(4), pp.820-828,2003, HongKong.
[34]David G Avellaneda M. and Mallat S.. Adaptive greedy approximation. Constr. Approx., 13(1), pp.57-98,1997.
[35]Candes E. and Donoho D.. New tight frames of curvelets and optimal representations of objects with C2 singularities[J]. Tech. rep., Standford University,2002,37.
[36]Ronald R. Coifman and Mladen V. Wickerhauser. Entropy-based algorithms for best basis selection[J]. IEEE Trans. Information Theory,38(2), pp.713-718, Mar.1992.
[37]S. Mallat, Z. Zhang. Matching Pursuit with Time Frequency Dictionaries [J]. IEEE Trans, sign. Proc.,41(12), pp.3397-3415,1993.
[38]S. Chen and D.L. Donoho. Basis Pursuit[J]. Journal of IEEE, pp.41-44,1995.
[39]S. Chen, D.L. Donoho and M.A. Saunders. Atomic decomposition by basis pur-suit[J]. SIAM J. Sci. Comput.,20(1), pp.33-61,1998.
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