Variation sparse source imaging based on conditional mean for electromagnetic extended sources

VSSI-GGD: A Variation Sparse EEG Source Imaging Approach Based on Generalized Gaussian Distribution

Electroencephalographic (EEG) source imaging (ESI) is a powerful method for studying brain functions and surgical resection of epileptic foci. However, accurately estimating the location and extent of brain sources remains challenging due to noise and background interference in EEG signals. To reconstruct extended brain sources, we propose a new ESI method called Variation Sparse Source Imaging based on Generalized Gaussian Distribution (VSSI-GGD). VSSI-GGD uses the generalized Gaussian prior as a sparse constraint on the spatial variation domain and embeds it into the Bayesian framework for source estimation. Using a variational technique, we approximate the intractable true posterior with a Gaussian density. Through convex analysis, the Bayesian inference problem is transformed entirely into a series of regularized L2p -norm ( ) optimization problems, which are efficiently solved with the ADMM algorithm. Imaging results of numerical simulations and human experimental dataset analysis reveal the superior performance of VSSI-GGD, which provides higher spatial resolution with clear boundaries compared to benchmark algorithms. VSSI-GGD can potentially serve as an effective and robust spatiotemporal EEG source imaging method. The source code of VSSI-GGD is available at https://github.com/Mashirops/VSSI-GGD.git.

Electrophysiological brain imaging based on simulation-driven deep learning in the context of epilepsy

Identifying the location, the spatial extent and the electrical activity of distributed brain sources in the context of epilepsy through ElectroEncephaloGraphy (EEG) recordings is a challenging task because of the highly ill-posed nature of the underlying Electrophysiological Source Imaging (ESI) problem. To guarantee a unique solution, most existing ESI methods pay more attention to solve this inverse problem by imposing physiological constraints. This paper proposes an efficient ESI approach based on simulation-driven deep learning. Epileptic High-resolution 256-channels scalp EEG (Hr-EEG) signals are simulated in a realistic manner to train the proposed patient-specific model. More particularly, a computational neural mass model developed in our team is used to generate the temporal dynamics of the activity of each dipole while the forward problem is solved using a patient-specific three-shell realistic head model and the boundary element method. A Temporal Convolutional Network (TCN) is considered in the proposed model to capture local spatial patterns. To enable the model to observe the EEG signals from different scale levels, the multi-scale strategy is leveraged to capture the overall features and fine-grain features by adjusting the convolutional kernel size. Then, the Long Short-Term Memory (LSTM) is used to extract temporal dependencies among the computed spatial features. The performance of the proposed method is evaluated through three different scenarios of realistic synthetic interictal Hr-EEG data as well as on real interictal Hr-EEG data acquired in three patients with drug-resistant partial epilepsy, during their presurgical evaluation. A performance comparison study is also conducted with two other deep learning-based methods and four classical ESI techniques. The proposed model achieved a Dipole Localization Error (DLE) of 1.39 and Normalized Hamming Distance (NHD) of 0.28 in the case of one patch with SNR of 10 dB. In the case of two uncorrelated patches with an SNR of 10 dB, obtained DLE and NHD were respectively 1.50 and 0.28. Even in the more challenging scenario of two correlated patches with an SNR of 10 dB, the proposed approach still achieved a DLE of 3.74 and an NHD of 0.43. The results obtained on simulated data demonstrate that the proposed method outperforms the existing methods for different signal-to-noise and source configurations. The good behavior of the proposed method is also confirmed on real interictal EEG data. The robustness with respect to noise makes it a promising and alternative tool to localize epileptic brain areas and to reconstruct their electrical activities from EEG signals.

Probabilistic Structure Learning for EEG/MEG Source Imaging With Hierarchical Graph Priors

Brain source imaging is an important method for noninvasively characterizing brain activity using Electroencephalogram (EEG) or Magnetoencephalography (MEG) recordings. Traditional EEG/MEG Source Imaging (ESI) methods usually assume the source activities at different time points are unrelated, and do not utilize the temporal structure in the source activation, making the ESI analysis sensitive to noise. Some methods may encourage very similar activation patterns across the entire time course and may be incapable of accounting the variation along the time course. To effectively deal with noise while maintaining flexibility and continuity among brain activation patterns, we propose a novel probabilistic ESI model based on a hierarchical graph prior. Under our method, a spanning tree constraint ensures that activity patterns have spatiotemporal continuity. An efficient algorithm based on an alternating convex search is presented to solve the resulting problem of the proposed model with guaranteed convergence. Comprehensive numerical studies using synthetic data on a realistic brain model are conducted under different levels of signal-to-noise ratio (SNR) from both sensor and source spaces. We also examine the EEG/MEG datasets in two real applications, in which our ESI reconstructions are neurologically plausible. All the results demonstrate significant improvements of the proposed method over benchmark methods in terms of source localization performance, especially at high noise levels.

Higher Resolution sLORETA (HR-sLORETA) in EEG Source Imaging

sLORETA is one of the well-established EEG source localization methods that is popular for its satisfactory estimation, simplicity, and fast computation. However, the method has a low-resolution and requires manual post-processing thresholding to provide a sparser solution with acceptable resolution in source detection. Here we propose a subspace based thresholding that results in a higher resolution brain imaging based on minimizing a desired least square source detection error. Simulation results show the proposed method, denoted by HR-sLORETA, provides stable and high resolution solution in terms of Percentage of Undetected Sources (PUS) and Spatial Dispersion (SD) compared to the existing manual thresholding approaches as well as Otsu thresholding approach. It is shown that HR-sLORETA outperforms Otsu, which is the only other available automatic thresholding method, in scenarios with three or more sources.

Bayesian Electromagnetic Spatio-Temporal Imaging of Extended Sources Based on Matrix Factorization

Accurate estimation of the locations and extents of neural sources from electroencephalography and magnetoencephalography (E/MEG) is challenging, especially for deep and highly correlated neural activities. In this study, we proposed a new fully data-driven source imaging method, source imaging based on spatio-temporal basis function (SI-STBF), which is built upon a Bayesian framework, to address this issue. The SI-STBF is based on the factorization of a source matrix as a product of a sparse coding matrix and a temporal basis function (TBF) matrix, which includes a few TBFs. The prior of the TBF is set in the empirical Bayesian manner. Similarly, for the spatial constraint, the SI-STBF assumes the prior covariance of the coding matrix as a weighted sum of several spatial covariance components. Both the TBFs and the coding matrix are learned from E/MEG simultaneously through variational Bayesian inference. To enable inference on high-resolution source space, we derived a scalable algorithm using convex analysis. The performance of the SI-STBF was assessed using both simulated and experimental E/MEG recordings. Compared with L₂-norm constrained methods, the SI-STBF is superior in reconstructing extended sources with less spatial diffusion and less localization error. By virtue of the spatio-temporal factorization of source matrix, the SI-STBF also produces more accurate estimations than spatial-only constraint method for high correlated and deep sources.