Research Of EEG Analysis Based On L_p(0<p?1) Norm

The understanding of information processing mechanisms in the brain is a hot topic in the field of cognitive neuroscience research.It has played a predominant role in both promoting the brain protection and the enhancement of brain function.Due to its easy acquisition and millisecond temporal resolution,Electroencephalography(EEG)has been widely applied in the related researches,such as cognitive studies,clinical diagnose,and brain computer interface,etc.In the field of EEG analysis,power spectral analysis,brain network construction and feature recognition,have been widely used to extract the modulation of oscillation rhythm,the pattern of information transmission,and the discriminative features.However,EEG signal is usually contaminated by various artifacts due to eye blinks,head movement and the loose contact of electrodes.These artifacts will greatly influence EEG analysis and mislead researchers in understanding the underlying brain mechanism.In essence,EEG based analysis such as autoregressive model,Granger causality and graph embedding analysis are designed in the L2 norm space which are prone to the influence of outliers because of its square property.In this work,we proposed to design the autoregressive model,brain network estimation and feature recognition methods in the Lp(0<p?1)-norm space,aiming to develop a series of robust methods so as to restrict the influence of outliers.The contribution of this dissertation is as follows.1.Based on the theory of autoregressive model,we developed the Lp(0<p?1)-norm based autoregressive model(Lp AR),and utilized quasi-newton method to solve the corresponding parameters.This method can restrict outliers in parameter estimation so as to offer reliable results in both signal prediction and power spectral estimation.2.To implement the directed network analysis for scalp EEG robustly,we firstly estimated the multivariate autogressive(MVAR)model parameters in the Lp(0<p?1)-norm.Based on these estimated coefficients,we further developed robust network analysis in the time domain(Lp(0<p?1)-norm based Granger causality analysis,Lp GCA)and frequency domain(Lp(0<p?1)-norm based partial directed coherence,Lp PDC).Both the simulation studies and the application to the real EEG dataset contaminated with strong ocular artifacts consistently demonstrate that the developed two approaches could restrict the artifacts influence,and estimate the more accurate directed networks for scalp EEG.3.To estimate time-varying networks robustly,we developed the L1-norm based adaptive directed transfer function(L1 ADTF).L1 ADTF newly defined the state estimation equation for the Kalman filter algorithm with L1 norm and utilized the alternating direction method of multipliers(ADMM)to estimate the time-varying multivariate coefficients in the L1 norm space.Based on these coefficients,we calculated the DTF factors inferred at each time point to construct time-varying networks.The results in both simulation studies and real motor imagery(MI)EEG dataset contaminated with strong ocular artifacts proved that L1 ADTF could robustly capture the underlying state transformations in a dynamic system and estimate the time varying brain networks during cognitive procedure robustly.4.To carry out reliable recognition from EEG features with outlier,we developed L1 norm based graph embedding(L1 GE).This method defined the graph embedding structure in the Ll-norm space and utilized the maximization strategy to estimate model parameters.Compared with other graph embedding extensions,L1 GE can estimate the classification hyper planes more robustly from outlier-noised data samples and get better classification results for MI EEG datasets.In conclusion,this dissertation combined autoregressive model,Granger causality analysis and graph embedding with Lp(0<p<1)norm and developed a series of robust approaches to restrict the artifacts influence on EEG analysis.These methods offered alternatives to traditional EEG analysis in artifacts conditions.