A Study On Electromagnetic Source Imaging Based On Bayesian Probabilistic Model And Deep Neural Network

Electroencephalography(EEG)and Magnetoencephalography(MEG)are the merely noninvasive techniques that provide millisecond-scale temporal resolution and wholebrain coverage.Hence,they have been widely used in multiple applications,including cognitive function study and psychiatric disorders diagnosis.However,due to the volume conduction effect,E/MEG measurements are with relatively low spatial resolution.Electromagnetic source imaging(ESI)is an important method to boost the spatial resolution,which reconstructs the neural activity over cortex from E/MEG measurements.ESI is of great importance for the tasks where accurate identification of both locations and extents of the rapid brain dynamics is necessary,such as delineation of the epileptogenic zone in epilepsy patients.To acquire satisfactory spatial resolution in distributed source model,there are enormously more fixed dipoles than sensors.Meanwhile,the inverse problem is severely illposed and appropriate prior constraints are essential to acquire the meaningful solution in the context of neurophysiology.Source imaging algorithms can the framed into three categories: regularization based algorithms can be easily formulated but different regularization terms should balanced with carefully specified hyperparameters,by which the estimation is significantly influenced;Bayesian probabilistic model based algorithms are relatively more complicated in modeling where prior assumptions are incorporated into the graphical structure.The algorithms are more robust and typically require less hyperparameters.However,the long inference time limits their real-time applications;neural network based algorithm formulates the mapping from measurements to the sources with little inference time.But how to integrate the neurophysiologic knowledge into the network and how to generate the training data still remain the issues.In this thesis,based on the Bayesian probabilistic model and deep neural networks,we proposed several novel source imaging algorithms and frameworks.Specifically,the main contributions are as follows:1.Under the Bayesian probabilistic model,we propose SI-SST(source imaging with smoothness in spatial and temporal domains),in which the smoothness is imposed in both spatial and temporal domain,via the employment of a spatial smoothing kernel and an autoregressive model respectively.Precision parameter of the sparseness encoding variables are constructed based on overlapped clusters derived from data driven parcellization over the cortex.Because the convexity-based update rule becomes invalid in this situation,we propose novel update formulas based on the fixed-point criterion.Entire variables and parameters can be updated in a data-driven fashion under empirical Bayesian framework.Numerical simulations show that,compared to the benchmark methods,SI-SST has the superior imaging performance for the extended sources within a wide range of extents,and is robust to the noise intensities.Furthermore,SI-SST is capable to extract meaningful high-frequency information from the severely corrupted signal.2.Based on Bayesian probabilistic model,We propose a novel construction manner of the spatial smoothing kernel,LASSK(linear adaptive spatial smoothing kernel),where the smoothing kernel is defined as the linear combination of specific smoothing matrices.Coefficients are updated under the empirical Bayesian framework by iteratively solving linear equations,which demands much less computational cost than inverting a huge sparse matrix in BESTIES(Bayesian electromagnetic spatio-temporal imaging of extended sources).Numerical simulations show that,compared to BESTIES,LASSK achieves genuinely adaptive spatial smoothness and becomes much more robust to the initialization.3.We propose a novel source imaging framework,SI-SBLNN(source imaging framework with a combination of sparse Bayesian learning and deep neural network),in which the neural network is incorporated into a source imaging algorithm based on sparse Bayesian learning through constructing the mapping from measurements to precision parameters.Using this mapping,the variational inference can be substantially compressed with much less computational cost.Training data,which inherit the prior spatial properties of hierarchical probabilistic model,can be synthesized by conducting the top-down ancestral sampling.Compared to the purely neural network based algorithm,SI-SBLNN is less struggling in network training and capable to obtain better imaging results for head models with high spatial resolution.4.Under the variational Bayesian framework,we propose a novel multi-trial E/MEG source imaging algorithm,MT-SBL(multi-trial sparse Bayesian learning).MT-SBL constructs the hierarchical Bayesian probabilistic model,where the deep latent variables are enforced prior distributions with shared learnable parameters and distinct variational posterior distributions across different trials.Log Normal distribution is employed to model the uncertainty of sources intensity.MT-SBL has significantly upgraded performance when more trials are included and is capable to extract specific information from measurement across trials as SNIR increases.