广义特征分解盲源分离算法的若干问题研究
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摘要
盲源分离是指在信号源和传输信道完全或部分未知情况下,只利用传感器阵的观测数据来分离、提取源信号的方法。近年来,已成为信号处理和神经网络领域的一个研究热点。盲分离在无线通信、雷达、声纳、语音信号处理、医学信号处理、图像处理等方面有着广泛的应用。本文围绕这一热点课题展开,重点研究了基于二阶统计量的广义特征值盲分离算法,主要做了以下几方面工作:
(1)针对含噪信号的盲源分离问题,将小波变换去噪的方法应用于盲源分离方法的预处理过程。在总结分析多种小波变换去噪方法优缺点的基础上,将基于卷积型小波包变换的多尺度降噪方法用于对含噪盲信号进行预处理,保证了含噪信号盲源分离的精度。
(2)提出了一种基于二进小波变换的广义特征值盲分离算法,该算法通过对混合信号的二进小波变换,增强了信号间的非高斯性,在此基础上运用广义特征分解对混合信号进行分离,能够获得较高的分离精度。
(3)针对非平稳混合信号的分离,提出基于EMD分解的广义特征值盲分离算法。EMD分解具有比小波变换更高的时频分辨率且不会发生频谱泄漏,将其与广义特征值盲分离算法结合,对非平稳混合信号有更好的分离效果。同时EMD能够自适应的分解信号,克服了小波变换中需选择小波基的困难,使得算法简单,适用性强。
(4)针对非线性盲源分离问题,将线性广义特征分解盲分离算法扩展到了非线性领域。利用核函数将混合信号投影到高维特征空间,将样本空间的非线性混合问题转化成非线性特征空间的线性混合问题,再用基于二进小波变换的广义特征值盲分离法进行求解,能够获得较高的分离精度。算法对源信号的概率密度分布不必进行过多的假设,且不需要进行最优化迭代,故简单易实现。
Blind source separation (BSS) is to separate the source signals from the mixing signals without prior knowledge of the source signals and the transmission condition. It has been a focus in the research area of signal processing and neural networks. And it has been widely used in wireless communication, sonar and radar systems, medical signals processing, image processing, and so on. In this dissertation, the algorithm of the blind source separation based on generalized eigendecomposition is mainly investigated. The primary contributions and original ideas included in this dissertation are summarized as below.
(1)For the problem of the blind source separation of noised signals, wavelet de-noising algorithms are applied in the pretreatment process of BSS. Based on summarizing and analyzing the advantages and shortcomings of various methods, a multi-scale de-noising algorithm based on the convolution type wavelet packet transform is presented to be applied in the pretreatment process of BSS. The algorithm ensures the precision of the noisy BSS model.
(2)Blind source separation based on generalized eigendecomposition using dyadic wavelet is proposed. By the method of dyadic wavelet transform, the mixing signals may be highly non-gaussian. In the meantime, the transacted signals are separated by the method of generalized eigendecomposition. Effectivity and performance of the new algorithm are demonstrated by the computer simulations.
(3)In view of the limitations of the current generalized eigendecomposition blind source separation methods for the non-stationary signals, a new method for blind source separation based on the generalized eigendecomposition using empirical mode decomposition (EMD) is presented. In comparison to wavelet transform, EMD has more predominance about time-frequency resolution and will not cause spectrum-leakage influences, so better separation results to non-stationary signals are obtained by the new algorithm. Avoiding the wavelet base selection, the algorithm is more simple and easy to implement due to the adaptivity of EMD.
(4)According to nonlinear BSS problem, linear BSS algorithm based on generalized eigendecomposition is extended to nonlinear cases. By the use of kernel function, the mixing signals are mapped to high-dimensional feature space, and the nonlinear mixing model in sample space is transformed to a linear mixing model in nonlinear feature space. Then BSS based on generalized eigendecomposition using dyadic wavelet is employed to separate the mapped signals. The new algorithm dose not hypothesizes too much about the probability density of source signals, and optimal iterative isn’t applied in the procedure. So the algorithm is easy to implement.
(1)针对含噪信号的盲源分离问题,将小波变换去噪的方法应用于盲源分离方法的预处理过程。在总结分析多种小波变换去噪方法优缺点的基础上,将基于卷积型小波包变换的多尺度降噪方法用于对含噪盲信号进行预处理,保证了含噪信号盲源分离的精度。
(2)提出了一种基于二进小波变换的广义特征值盲分离算法,该算法通过对混合信号的二进小波变换,增强了信号间的非高斯性,在此基础上运用广义特征分解对混合信号进行分离,能够获得较高的分离精度。
(3)针对非平稳混合信号的分离,提出基于EMD分解的广义特征值盲分离算法。EMD分解具有比小波变换更高的时频分辨率且不会发生频谱泄漏,将其与广义特征值盲分离算法结合,对非平稳混合信号有更好的分离效果。同时EMD能够自适应的分解信号,克服了小波变换中需选择小波基的困难,使得算法简单,适用性强。
(4)针对非线性盲源分离问题,将线性广义特征分解盲分离算法扩展到了非线性领域。利用核函数将混合信号投影到高维特征空间,将样本空间的非线性混合问题转化成非线性特征空间的线性混合问题,再用基于二进小波变换的广义特征值盲分离法进行求解,能够获得较高的分离精度。算法对源信号的概率密度分布不必进行过多的假设,且不需要进行最优化迭代,故简单易实现。
Blind source separation (BSS) is to separate the source signals from the mixing signals without prior knowledge of the source signals and the transmission condition. It has been a focus in the research area of signal processing and neural networks. And it has been widely used in wireless communication, sonar and radar systems, medical signals processing, image processing, and so on. In this dissertation, the algorithm of the blind source separation based on generalized eigendecomposition is mainly investigated. The primary contributions and original ideas included in this dissertation are summarized as below.
(1)For the problem of the blind source separation of noised signals, wavelet de-noising algorithms are applied in the pretreatment process of BSS. Based on summarizing and analyzing the advantages and shortcomings of various methods, a multi-scale de-noising algorithm based on the convolution type wavelet packet transform is presented to be applied in the pretreatment process of BSS. The algorithm ensures the precision of the noisy BSS model.
(2)Blind source separation based on generalized eigendecomposition using dyadic wavelet is proposed. By the method of dyadic wavelet transform, the mixing signals may be highly non-gaussian. In the meantime, the transacted signals are separated by the method of generalized eigendecomposition. Effectivity and performance of the new algorithm are demonstrated by the computer simulations.
(3)In view of the limitations of the current generalized eigendecomposition blind source separation methods for the non-stationary signals, a new method for blind source separation based on the generalized eigendecomposition using empirical mode decomposition (EMD) is presented. In comparison to wavelet transform, EMD has more predominance about time-frequency resolution and will not cause spectrum-leakage influences, so better separation results to non-stationary signals are obtained by the new algorithm. Avoiding the wavelet base selection, the algorithm is more simple and easy to implement due to the adaptivity of EMD.
(4)According to nonlinear BSS problem, linear BSS algorithm based on generalized eigendecomposition is extended to nonlinear cases. By the use of kernel function, the mixing signals are mapped to high-dimensional feature space, and the nonlinear mixing model in sample space is transformed to a linear mixing model in nonlinear feature space. Then BSS based on generalized eigendecomposition using dyadic wavelet is employed to separate the mapped signals. The new algorithm dose not hypothesizes too much about the probability density of source signals, and optimal iterative isn’t applied in the procedure. So the algorithm is easy to implement.
引文
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3. Charkani N,Deville Y.Self-adaptive separation of convolutively mixed signals with a recursive structure,Part I:Stability analysis and optimization of the asymptotic behavior[J]. Signal Processing,1999,73:225-254
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5. Mathews V J,Xie Z.A stochastic gradient adaptive filter with gradient adaptive step size.IEEE Trans[J].Signal Processing, 1993,41:2075-2087
6. He Z Y,Liu J,and Yang L X.Blind separation of images using edgeworth expansion based on ICA algorithm[J].Chinese Journal of Electronics,1999,8(3):278-282
7. Hyvarinen A,Karhunen J,and Oja E.Independent component analysis[M],New York: Wiley, 2001
8.高颖.盲源分离理论及其在地球物理勘探中的应用[D]:[博士学位论文].吉林:吉林大学, 2008
9. Hyvarinen A,Oja E.Independent component analysis: algorithms and applications[J]. Neural Networks,2000,13:411-430
10.张贤达,保铮.盲信号分离.电子学报,2001,29(12):1767-1771
11. Hyvarinen A.Fast and Robust fixed-point algorithms for Independent Component Analysis[J]. IEEE Trans.on Neural Networks.1999.10(3):626-634
12.胡英.盲分离算法研究及其在图像处理中的应用[D]:[博士学位论文].上海:上海交通大学,2003
13. Comon P.Independent component analysis, a new concept? [J]. Signal Processing,1994,36: 287-314
14. Jutten C,Herault J.Blind separation of sources,Part I:an adaptive algorithm based on neuromimetic architecture[J].Signal Processing,1991,24(1):1-10
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17. Zhang L Q, Amari S,and Cichocki A.Semiparametric model and superefficiency in blind deconvolution[J].Signal Processing,2001,8:2535-2553
18. Amari S.Estimating Functions of Independent Component Analysis for Temporally Correlated Signals[J]. Neural Computation,2000,12:1155-1179
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