Research On EEG Source Imaging Methods Based On Bayesian Theory And Spatio-Temporal Constraints

Electroencephalography(EEG)is an important technique for brain functional imaging.EEG has plenty of advantages,such as non-invasive,non-radioactive,high temporal resolution and economical efficiency.Therefore,EEG has been widely used in cognitive neuroscience and clinical context.The task to reconstruct cortex activities from the EEG signals on the scalp is referred to as EEG source imaging.Accurate estimating locations and extents of cortical activities helps improve the understanding of the basic mechanisms of cognitive processes and characterizations of pathologies that impair normal function.In clinic,such as epilepsy treatment,accurately determining the locations and extents of lesions is greatly significant for surgical treatments.EEG source imaging is an severely ill-posed problem and exists infinite possible solutions which satisfy the EEG recordings.Therefore,to obtain a unique estimation,prior constraints are necessary to narrow the solution space.Traditional methods includes the2-norm based algorithms and sparse constrained algorithms.However,the estimations of 2-norm based algorithms are too blurred compared to the ground truth,and are not sensitive to the source extents.In contrast,the solutions of sparse constrained methods are too focal,and can not reconstruct the extents of cortex activity.Hence,estimating the locations and spatial extents of brain sources accurately remains to be a long-standing challenge.EEG signals present abundant temporal information,which can be incorporated to improve the performance of source imaging as shown by previous studies.In this thesis,with the help of Bayeisn inference and convex optimization techniques,we proposed several EEG source imaging algorithms using spatio-temporal constraint under the Bayesian probabilistic framework to reconstruct the brain activities more accurately.More specifically,the contributions of this thesis are fourfold:1.A new method,STRAPS(spatio-temporally regularized algorithm for M/EEG patch source imaging),is proposed based on the state space model under the Bayesian probabilistic framework.STRAPS utilizes a multivariate auto-aggressive model to describe the spatial and temporal correlations between sources.Considering the memory and computational challenge of Kalman filtering,STRAPS employs the recursive penalized least-squares to obtain the approximated solutions.STRAPS recovers the locations,extents and time courses of sources more accurately than traditional methods.Compared to the algorithm with similar model,STRAPS obtains satisfied estimations,but has much less computational and memory requirements.2.Under the empirical Bayesian framework,we propose BESTIES(Bayesian Electromagnetic Spatio-Temporal Imaging of Extended Sources),which is based on Markov random field(MRF)and temporal basis functions(TBFs),to reconstruct extended sources.BESTIES employs MRF to model the spatial relationship between sources,the temporal smoothness of which is modeled by the TBFs.Using variational Bayesian and convex optimization,we obtain a fully data-driven algorithm.Both the MRF parameter and the contribution of each TBF to sources are determined by EEG recordings.Compared to traditional 2norm based and sparse constrained methods,BESTIES obtains more accurate estimations of the spatial and temporal patterns of brain activities.3.Under the Bayesian probabilistic framework,we propose a new source imaging method,VSSI-CM(Variation Sparse Source Imaging based on Conditional Mean for Electromagnetic Extended Sources),which is based on variation sparseness and TBFs.VSSI-CM explores sparseness of current sources in the variation domain(differences between neighbored sources),which is achieved by the Laplace prior distribution,to reconstruct source extents.For the temporal domain,VSSI-CM projects EEG data and current sources into the subspace spanned by several TBFs.Instead of the traditional MAP estimations,VSSI-CM proposes the conditional mean of the posterior as the source estimation.According to convex analysis,the Laplace distribution is represented by a maximum over Gaussian functions of varying scales.By double-loop algorithm,VSSI-CM is also a fully data-driven algorithm.According to simulation results,compared to traditional algorithms,VSSI-CM estimates source locations and extents more accurately.Additionally,VSSI-CM also obtains better estimations than MAP.4.Under the empirical Bayesian framework,we propose STBFSI(Spatio-Temporal Basis Functions Source Imaging),which is based on the notion of matrix decomposition,to reconstruct extended sources.STBFSI decomposes the current sources as the linear combination of several unknown TBFs.For the spatial constraint,we consider the prior covariance of sources as a weighted sum of several covariance bases,as emperical Bayesian.According to ARD(automatic relevance determination),STBFSI automatically selects the covariance bases relevant to current sources,the number of TBF and the waveforms of each TBF.STBFSI provides an algorithm framework using spatio-temporal constraints for EEG source imaging.Based on STBFSI,it is flexible to apply the information of other imaging modalities,such as f MRI.