Sparse EEG Source Localization Under the Variational Bayesian Framework

We propose a new EEG source localization method that simultaneously performs SOurce and FOrward MOdel REconstruction (SOFOMORE) in a hierarchical Bayesian framework. Reconstruction of the forward model is motivated by the many uncertainties involved in the forward model, including the representation of the cortical surface, conductivity distribution, and electrode positions. We demonstrate in both simulated and real EEG data that reconstruction of the forward model improves localization of the underlying sources.

Complementary with electroencephalograph (EEG), functional magnetic resonance imaging (fMRI), with high spatial resolution, is powerful at providing prior source locations based on actual brain physiology. It hereby can help improve the accuracy of EEG source localization. However, most of the current methods directly penalize the sources whose fMRI activation probability is low and estimate the sources activities at every time point. Thus, they do not account for the temporal interrelated and non-stationary features of electromagnetic brain signals, and some are too much dependent on the fMRI prior. Here, we propose a new fMRI informed EEG source localization method and is termed fMRI-informed spatio-temporal unifying tomography (FIST). It uses a mixed norm constraint defined in terms of time–frequency decomposition of the sources and combines it with fMRI prior. The Fast Iterative Shrinkage Thresholding Algorithm is employed to solve the optimization problem. Both simulated and real EEG data are applied to assess the performance of the proposed method. Compared with L2-norm constrained methods, FIST has the superiority brain source estimation both in the spatial and temporal domains. By virtue of the fMRI information as a prior, FIST has great improvement in spatial accuracy and computational efficiency, when comparing with the method which only uses mixed-norm constraint. In addition, FIST shows good ability to select the fMRI priors to get a better estimation without totally depending on the prior, when comparing with the method which also has fMRI prior information.

Electroencephalogram (EEG) source localization requires a solution to an ill-posed inverse problem. The additional challenge is to solve this problem in the context of multiple moving sources. An effective and simple technique for both separation and localization of EEG sources is therefore proposed by incorporating an algorithmically coupled blind source separation (BSS) approach. The method relies upon having a priori knowledge of the locations of a subset of the sources. The cost function of the BSS algorithm is constrained by this information, and the unknown sources are iteratively calculated. An important application of this method is to localize abnormal sources, which, for example, cause changes in attention, movement, and behavior. In this application, the Alpha rhythm was considered as the known sources. Simulation studies are presented to support the potential of the approach in terms of source localization.

EEG source localization is an important technical issue in EEG analysis. Despite many numerical methods existed for EEG source localization, they all rely on strong priors and the deep sources are intractable. Here we propose a deep learning framework using spatial basis function decomposition for EEG source localization. This framework combines the edge sparsity prior and Gaussian source basis, called Edge Sparse Basis Network (ESBN). The performance of ESBN is validated by both synthetic data and real EEG data during motor tasks. The results suggest that the supervised ESBN outperforms the traditional numerical methods in synthetic data and the unsupervised fine-tuning provides more focal and accurate localizations in real data. Our proposed deep learning framework can be extended to account for other source priors, and the real-time property of ESBN can facilitate the applications of EEG in brain-computer interfaces and clinics.

One of the most important steps of pre-surgical diagnosis in patients with medically intractable epilepsy is to find the precise location of the epileptogenic foci. An Electroencephalography (EEG) is a non-invasive standard tool used at epilepsy surgery center for pre-surgical diagnosis. In this paper a modified particle swarm optimization (MPSO) method is applied to a real EEG data, i.e., a somatosensory evoked potentials (SEPs) measured from a healthy subject, to solve the EEG source localization problem. A high resolution 1 mm hexahedra finite element volume conductor model of the subject's head was generated using T1-weighted magnetic resonance imaging data. An exhaustive search pattern and the MPSO method were then applied to the peak of the averaged SEPs data. The non-invasive EEG source analysis methods localized the somatosensory cortex area where our clinical expert expected the received SEPs. The proposed inverse problem solver found the global minima with acceptable accuracy and reasonable number of iterations.

Source-space ICA for EEG source separation, localization, and time-course reconstruction

A crucial decision in designing a spatial sample for soil survey is the number of sampling locations required to answer, with sufficient accuracy and precision, the questions posed by decision makers at different levels of geographic aggregation. In the Indian Soil Health Card (SHC) scheme, many thousands of locations are sampled per district. In this paper the SHC data are used to estimate the mean of a soil property within a defined study area, e.g., a district, or the areal fraction of the study area where some condition is satisfied, e.g., exceedence of a critical level. The central question is whether this large sample size is needed for this aim. The sample size required for a given maximum length of a confidence interval can be computed with formulas from classical sampling theory, using a prior estimate of the variance of the property of interest within the study area. Similarly, for the areal fraction a prior estimate of this fraction is required. In practice we are uncertain about these prior estimates, and our uncertainty is not accounted for in classical sample size determination (SSD). This deficiency can be overcome with a Bayesian approach, in which the prior estimate of the variance or areal fraction is replaced by a prior distribution. Once new data from the sample are available, this prior distribution is updated to a posterior distribution using Bayes’ rule. The apparent problem with a Bayesian approach prior to a sampling campaign is that the data are not yet available. This dilemma can be solved by computing, for a given sample size, the predictive distribution of the data, given a prior distribution on the population and design parameter. Thus we do not have a single vector with data values, but a finite or infinite set of possible data vectors. As a consequence, we have as many posterior distribution functions as we have data vectors. This leads to a probability distribution of lengths or coverages of Bayesian credible intervals, from which various criteria for SSD can be derived. Besides the fully Bayesian approach, a mixed Bayesian-likelihood approach for SSD is available. This is of interest when, after the data have been collected, we prefer to estimate the mean from these data only, using the frequentist approach, ignoring the prior distribution. The fully Bayesian and mixed Bayesian-likelihood approach are illustrated for estimating the mean of log-transformed Zn and the areal fraction with Zn-deficiency, defined as Zn concentration <0.9 mg kg −1, in the thirteen districts of Andhra Pradesh state. The SHC data from 2015–2017 are used to derive prior distributions. For all districts the Bayesian and mixed Bayesian-likelihood sample sizes are much smaller than the current sample sizes. The hyperparameters of the prior distributions have a strong effect on the sample sizes. We discuss methods to deal with this. Even at the mandal (sub-district) level the sample size can almost always be reduced substantially. Clearly SHC over-sampled, and here we show how to reduce the effort while still providing information required for decision-making. R scripts for SSD are provided as supplementary material.

At the start of new operation, a production process is commonly unstable. Then, a process condition is into being stable gradually over time. For the purpose of shifting to mass production, the stability in a process should be evaluated. This paper proposes a method of evaluating the process stability based on Bayesian statistics and information theory. In Bayesian statistics, the knowledge for a process is renewed by deriving posterior distribution based on current prior distribution and observations. Here, equivalency between prior and posterior distributions could be considered to be a criterion for the stability in a process. It is needed to define difference between prior and posterior distributions in order to evaluate the equivalency between prior and posterior distributions. We first formulate the relation between the prior distribution and the posterior distribution for process mean using Bayesian statistics. Secondly, we evaluate the difference between the both distributions based on Kullback‐Leibler (K‐L) divergence in information theory. Finally, some numerical examples in the method of evaluating the stability in process mean are illustrated. Also, we discuss about a decision rule for the stability in process mean through the numerical investigation.

Conflict monitoring processes are central to cope with fluctuating environmental demands. However, the efficacy of these processes depends on previous trial history/experience, which is reflected in the "congruency sequence effect" (CSE). Several theoretical accounts have been put forward to explain this effect. Some accounts stress the role of perceptual processes in the emergence of the CSE. As yet, it is elusive how these perceptual processes are implemented on a neural level. We examined this question using a newly developed moving dots flanker task. We combine decomposition methods of EEG data and source localization. We show that perceptual processes modulate the CSE and can be isolated in neurophysiological signals, especially in the N2 ERP time window. However, mechanisms relating perception to action are also coded and modulated in this time window. We show that middle frontal regions (BA 6) are associated with processes dealing with purely perceptual processes. Inferior frontal regions (BA 45) are associated with processes dealing with stimulus-response transition processes. Likely, the neurophysiological modulations reflect unbinding processes at the perceptual level, and stimulus-response translation level needed to respond correctly on the presented (changed) stimulus-response relationships. The data establish a direct relationship between psychological concepts focusing on perceptual processes during conflict monitoring and neurophysiological processes using signal decomposition.

Three key cognitive components involved in deception, i.e., working memory, inhibition control and task switching share a most fundamental neuropsychological process, i.e., execution control. Although dissociable neuroanatomies associated with individual cognitive component for deception have been identified by fMRI, practical application of fMRI in lie detection remains constrained by its limited accessibility and low affordability, compared with which, EEG has greater advantages. However, fewer theoretical studies have been reported from EEG community and hence leads to the lack of EEG based knowledge on deception. This study therefore aims to propose new methods to extend the current EEG researches in deception by carrying out EEG source localization method combined with connectivity analysis on EEG data collected from fifteen subjects, who participated in a deception paradigm inducing both instructed lying (IL) and instructed truth-telling (IT) conditions. The results show that: (1) significant ERS in upper alpha band (10-12 Hz) in cuneus is observed for IL compared with IT condition, (2) event related connectivity strength between neural substrates responsible for execution control in executing selectively retrieving, monitoring and scrutinizing memory information is observed increased in upper alpha band for IL compared with IT condition, (3) regional and global clustering coefficient derived in connectivity analysis have shown strong correlation to the response time, and (4) relative higher upper alpha band power founded during self-reflection period may indicate sustained alertness.

EEG and MEG in mesial temporal lobe epilepsy: Where do the spikes really come from?

Background: Electroencephalography (EEG) may be used as an objective diagnosis tool for diagnosing various disorders. Recently, source localization from EEG is being used in the analysis of real-time brain monitoring applications. However, inverse problem reduces the accuracy in EEG signal processing systems. Objectives: This paper presents a new method of EEG source localization using variational mode decomposition (VMD) and standardized the low resolution brain electromagnetic tomography (sLORETA) inverse model. The focus is to compare the effectiveness of the proposed approach for EEG signals of depression patients. Method: As the first stage, real EEG recordings corresponding to depression patients are decomposed into various mode functions by applying VMD. Then, closely related functions are analyzed using the inverse modelling-based source localization procedures such as sLORETA. Simulations have been carried out on real EEG databases for depression to demonstrate the effectiveness of the proposed techniques. Results: The performance of the algorithm has been assessed using localization error (LE), mean square error and signal to noise ratio output corresponding to simulated EEG dipole sources and real EEG signals for depression. In order to study the spatial resolution for cortical potential distribution, the main focus has been on studying the effects of noise sources and estimating LE of inverse solutions. More accurate and robust localization results show that this methodology is very promising for EEG source localization of depression signals. Conclusion: It can be said that proposed algorithm efficiently suppresses the influence of noise in the EEG inverse problem using simulated EEG activity and EEG database for depression. Such a system may offer an effective solution for clinicians as a crucial stage of EEG pre-processing in automated depression detection systems and may prevent delay in diagnosis.

We introduce the prior model information to propose the regularized least-squares reverse time migration method (RLSRTM). The prior information is added into leastsquares reverse time migration (LSRTM) as the regularization term. The dynamic regularization parameter and scaling method to the regularization-term gradient is highlighted to ensure better constraint. To test the improvement of prior information to the inversion, LSRTM and RLSRTM is applied to a rough Marmousi model. The imaging results show that the prior information can improve the compensation to unbalanced illumination and precision of LSRTM. Moreover, the RLSRTM is more robust with low signal-to-noise ratio (SNR) data compared with the standard LSRTM.

To improve the EEG source localization in the brain, the conductivities used in the head model play a very important role. In this study, we focus on the modeling of the anisotropic conductivity of the white matter. The anisotropic conductivity profile can be derived from diffusion weighted magnetic resonance images (DW-MRI). However, deriving these anisotropic conductivities from diffusion weighted MR images of the white matter is not straightforward. In the literature, two methods can be found for calculating the conductivity from the diffusion weighted images. One method uses a fixed value for the ratio of the conductivity in different directions, while the other method uses a conductivity profile obtained from a linear scaling of the diffusion ellipsoid. We propose a model which can be used to derive the conductivity profile from the diffusion tensor images. This model is based on the variable anisotropic ratio throughout the white matter and is a combination of the linear relationship as stated in the literature, with a constraint on the magnitude of the conductivity tensor (also known as the volume constraint). This approach is stated in the paper as approach A. In our study we want to investigate dipole estimation differences due to using a more simplified model for white matter anisotropy (approach B), while the electrode potentials are derived using a head model with a more realistic approach for the white matter anisotropy (approach A). We used a realistic head model, in which the forward problem was solved using a finite difference method that can incorporate anisotropic conductivities. As error measures we considered the dipole location error and the dipole orientation error. The results show that the dipole location errors are all below 10 mm and have an average of 4 mm in gray matter regions. The dipole orientation errors ranged up to 66.4°, and had a mean of, on average, 11.6° in gray matter regions. In a qualitative manner, the results show that the orientation and location error is dependent on the orientation of the test dipole. The location error is larger when the orientation of the test dipole is similar to the orientation of the anisotropy, while the orientation error is larger when the orientation of the test dipole deviates from the orientation of the anisotropy. From these results, we can conclude that the modeling of white matter anisotropy plays an important role in EEG source localization. More specifically, accurate source localization will require an accurate modeling of the white matter conductivity profile in each voxel.

The brain-to-skull conductivity ratio (BSCR) is an important parameter in EEG source imaging and localization. Misspecification of this value may introduce localization errors in the estimation of brain electrical activity. However, the effect of this ratio has not been well understood despite many investigations. In the present study, we conducted a series of computer simulations to investigate the relationship between BSCR and EEG source localization accuracy. Furthermore, we have attempted to correlate the localization accuracy of epileptogenic regions with the BSCR in epilepsy patients. Our results indicate that the dipole localization errors ranged from 10 to 20 mm. The localization accuracy resulting when the conductivity ratio used in the inverse calculation was set at 20 was better than those resulting when the ratio was set at 80 in epilepsy patients with a deep tumor. Future work is needed to validate this finding by experimental investigations in a large patient population.