Study On Tensor Spatio-spectral Analysis Methods For Motor Imagery-based EEG Signals

Electroencephalography(EEG)signals modulated by motor imagery(MI)contain abundant rhythmic information related to brain activity.MI-based Brain-computer interface(BCI)has great prospects in the fields of medical rehabilitation and neural engineering.Currently,the widespread application of MI-BCI system is limited by its low decoding accuracy.Spatio-spectral analysis methods,which decode the rhythmic features related to MI activity by spatial and spectral information optimization,can enhance the decoding performance of EEG signals effectively.However,most of the existing methods represented by spatio-spectral filtering are oriented for two-way data,and hence are not always a good match for the EEG signals naturally born with complex multi-way structure.As a result,they are hard to sufficiently explore the cross-dimensional neural information of the EEG signals,and cannot accurately quantify the polyrhythmic oscillation of MI-EEG signals,thereby cannot meet the application requirement of BCI system.To address this issue,this thesis studies the spatio-spectral analysis methods based on tensor decomposition.A polyrhythmic synchronization model is proposed,and then three spatio-spectral analysis methods under the framework of the proposed model are respectively designed to mine the discriminative information,polyrhythmic synchronization-based amplitude and phase information,and polyrhythmic synchronization-based amplitude-phase coupling information of EEG signals in multi-way structure.Compared with the state of the art methods,our methods can exploit the information preserved in EEG signals more sufficiently,and achieve better decoding accuracies.The proposed methods are expected to provide a basic reference framework for further study.Specific research is listed as follows:Firstly,a polyrhythmic synchronization model is studied to reflect the complex synchronization and coupling of the rhythms contained in MI-based EEG signals.Based on tensor decomposition,this model combines the advantages of strong interpretability of PARAFAC and high flexibility of Tucker decomposition,and lays a foundation for the following multi-way structure-based spatio-spectral decoding methods.Secondly,the feature optimization of MI-based EEG signals is studied under multiway structure.In order to quantitative measurement of the non-stationary MI-EEG oscillations effectively,the spectrum-weighted tensor discriminant analysis(Sw TDA)is proposed to excavate rhythm information preserved in MI-EEG signals with multiway structures.The proposed Sw TDA method extracts discriminative features with joint optimization of spatial–spectral–temporal patterns based on Fisher discrimination criterion and residual iteration,and hence improve the accuracy of decoding MI-EEG signals.Thirdly,the polyrhythmic synchronization characteristics of MI-based EEG signals are studied.A tensor-based spatial spectral filtering(TSSF)is proposed to automatically learn the spectral filters for each EEG channel in conjunction with the corresponding spatial filter,based on tensor subspace analysis and the simultaneous diagonalization of the covariance matrices of EEG signals.The proposed TSSF method tries to maximumly utilize the rhythm information between EEG channels,and then improve the decoding performance of MI-EEG signals.Finally,the amplitude-phase coupling characteristics of MI-based EEG signals are studied under polyrhythmic synchronization.A common amplitude-phase measurement(CAPM)method based on Riemannian manifolds is proposed to achieve the joint measurement of EEG phase and amplitude information.The proposed CAPM method comprises a two-step approach.In the stage of feature extraction,a novel Riemannian graph embedding is proposed for dimensionality reduction and extracting the amplitude-phase coupling information of polyrhythmic synchronization.Therefore,it combines the advantages of tensor methods preserving the global structural information of EEG signals and the Riemannian manifold methods preserving the local structure of the samples.In the classification stage,a novel classifier is designed to incorporate the regularized linear regression in the computation of Riemannian distance for enhancing robustness.