脑电信号非线性分析方法的研究
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摘要
本文分别采用非线性动力学、小波变换、神经网络和混沌理论等现代分析方法对EEG信号的非线性特征进行了比较全面的分析和研究。这些分析方法都是当今非线性信号分析领域备受关注的新方法。随着信息科学和计算技术的发展，这些方法具有广阔的应用前景和潜在的优势。本文的主要贡献归纳如下：1)在小波变换的基础上，用150例EEG样本计算了表征EEG信号奇异性大小的Lipschitz指数。得出癫痫EEG的Lipschitz指数总体上比健康EEG小的结论，并分别作出健康EEG和癫痫EEG的Lipschitz指数谱。2)将基于高阶统计(HOS)的高阶奇异谱分析(HSSA)方法用于EEG信号的分析中，有效地克服了二阶奇异谱无法反映EEG信号非线性特征的缺陷。本文还利用小波多尺度信号分解和重构技术得出EEG的高阶奇异谱，实验结果表明该方法效果更好。3)在用PCA方法证实多通道EEG之间存在串扰的情况下，将ICA方法用于多通道EEG信号的盲源分离(BSS)。同时，将小波变换技术与ICA技术结合，有效地解决了现有ICA方法不能将噪声从信号中分离的问题。此外，为了提高算法的稳健性，本文提出采用双网络的方法并对ICA神经算法进行改进。4)提出相空间态密度和态方差的概念，并求出基于相对距离协方差矩阵的EEG奇异谱，求出基于相空间相对距离的EEG近似熵和信息熵。5)从相空间重构的角度解释了小波变换的物理本质，从而揭示：混沌时间序列的小波变换实质上是在重构的相空间中，混沌吸引子向小波滤波器向量所张的空间中的投影，这些结果与Packard等人提出的相空间重构方法本质上是一致的。本文还从小波空间导出延迟时间空间的向量方程。6)设计了两级Kohonen网络和小波网络的EEG信号分类的网络结构，并对算法进行详细的描述。
此外，有参考价值的工作还有：1)提出EEG信号相空间中无标度区会随嵌入维数而发生移动的观点。2)对多通道EEG信号的混叠问题和“独立源”概念作出物理解释。3)提出从延迟时间空间到小波空间的空间旋转问题，为从两个空间寻找混沌吸引子相轨道的共同点提供新的途径。4)得出未发现EEG具有低维混沌的结论。本文所有的计算均采用工具软件Matlab完成。
We investigated the nonlinear features of EEG in a relatively all-sided way by using current analysis methods such as nonlinear dynamics, wavelet transform, neural network and chaos theory respectively. These new methods are now become more concerned in the area of nonlinear signal analysis, and have a wide application prospect and potential advantage with the development of information science and computation technology. The main contribution of this thesis include: 1) Based on the wavelet transform, we calculated the Lipschitz exponents of EEG of 150 subjects, which characterize the singularity of EEG, and concluded that the Lipschitz exponents of epileptic EEG is larger than the one of normal EEG. We also obtained the spectra of the Lipschitz exponent both normal EEG and epileptic EEG. 2) By using higher-order singular specturm analysis (HSSA) for the analysis of EEG, which is based on the higher-order statistics, hence, the deficiency that the second-order singular spectrum cann't characterize the nonlinearity of EEG is overcome effectively. Furthermore, we made the higher-order sepctrum of EEG by using wavelet transform techniques for multi-scale signal decomposition and reconstruction. The results show that the method proposed herein is better. 3) After verifying
the fact that there are crosstalks exist among multi-channel EEGs by principle component analysis, we used ICA (Independent Component Analysis) technique for blind source separation (BSS) of EEG. To resolve the problem that ICA cann't separate noise from signal, we also combined the ICA with wavelet transform for BSS of EEG. Moreover, in order to improve the robustness of algorithm, a two-stage neural network was constructed and the algorithm of ICA was improved. 4) Proposed two new concepts, called state density and state variance, and drawed the singular spectrum of EEG based on
the covariance matrix of relative distance. In addition, we calculated the approximate entropy(ApEn) and information entropy of EEG based on the relative distance in phasespace. 5) We explained the physical essence of wavelet transfrom from the viewpoint of phase reconstruction, i.e. the wavelet
transform of chaotic time series is essentially a projection of strange attractor on the axis of the wavelet space that filter vectors open, which in correspondance with the method of phasespace reconstruction proposed by Packard and his Co-workers. Additionally, the vector equation of time-delay space was derived from wavelet space. 6) The architecture of two-stage Kohonen network and wavelet network were designed, which can be used for classifying EEG, and the corresponding algorithm was described in detail.
Besides those mentioned above, other valuable work include: 1) A viewpoint was proposed that scale-invariant range of phasespace of EEG will be moved as the increase of the embedding dimension. 2) A physical explanation for both the aliasing and the "Independent Source" of EEG were given. 3) In order to seek a new approach to finding the common ground of phase trajectory of chaotic attractor between two spaces, the concept of phase space rotation between time-delay space and wavelet space was presented. 4) It was concluded that the low-dimension chaos in EEG isn't found in our works.
All computation work in this thesis are made under Matlab.
此外，有参考价值的工作还有：1)提出EEG信号相空间中无标度区会随嵌入维数而发生移动的观点。2)对多通道EEG信号的混叠问题和“独立源”概念作出物理解释。3)提出从延迟时间空间到小波空间的空间旋转问题，为从两个空间寻找混沌吸引子相轨道的共同点提供新的途径。4)得出未发现EEG具有低维混沌的结论。本文所有的计算均采用工具软件Matlab完成。
We investigated the nonlinear features of EEG in a relatively all-sided way by using current analysis methods such as nonlinear dynamics, wavelet transform, neural network and chaos theory respectively. These new methods are now become more concerned in the area of nonlinear signal analysis, and have a wide application prospect and potential advantage with the development of information science and computation technology. The main contribution of this thesis include: 1) Based on the wavelet transform, we calculated the Lipschitz exponents of EEG of 150 subjects, which characterize the singularity of EEG, and concluded that the Lipschitz exponents of epileptic EEG is larger than the one of normal EEG. We also obtained the spectra of the Lipschitz exponent both normal EEG and epileptic EEG. 2) By using higher-order singular specturm analysis (HSSA) for the analysis of EEG, which is based on the higher-order statistics, hence, the deficiency that the second-order singular spectrum cann't characterize the nonlinearity of EEG is overcome effectively. Furthermore, we made the higher-order sepctrum of EEG by using wavelet transform techniques for multi-scale signal decomposition and reconstruction. The results show that the method proposed herein is better. 3) After verifying
the fact that there are crosstalks exist among multi-channel EEGs by principle component analysis, we used ICA (Independent Component Analysis) technique for blind source separation (BSS) of EEG. To resolve the problem that ICA cann't separate noise from signal, we also combined the ICA with wavelet transform for BSS of EEG. Moreover, in order to improve the robustness of algorithm, a two-stage neural network was constructed and the algorithm of ICA was improved. 4) Proposed two new concepts, called state density and state variance, and drawed the singular spectrum of EEG based on
the covariance matrix of relative distance. In addition, we calculated the approximate entropy(ApEn) and information entropy of EEG based on the relative distance in phasespace. 5) We explained the physical essence of wavelet transfrom from the viewpoint of phase reconstruction, i.e. the wavelet
transform of chaotic time series is essentially a projection of strange attractor on the axis of the wavelet space that filter vectors open, which in correspondance with the method of phasespace reconstruction proposed by Packard and his Co-workers. Additionally, the vector equation of time-delay space was derived from wavelet space. 6) The architecture of two-stage Kohonen network and wavelet network were designed, which can be used for classifying EEG, and the corresponding algorithm was described in detail.
Besides those mentioned above, other valuable work include: 1) A viewpoint was proposed that scale-invariant range of phasespace of EEG will be moved as the increase of the embedding dimension. 2) A physical explanation for both the aliasing and the "Independent Source" of EEG were given. 3) In order to seek a new approach to finding the common ground of phase trajectory of chaotic attractor between two spaces, the concept of phase space rotation between time-delay space and wavelet space was presented. 4) It was concluded that the low-dimension chaos in EEG isn't found in our works.
All computation work in this thesis are made under Matlab.
引文
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