| 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 verifyingthe 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 onthe 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 wavelettransform 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.
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