Sparse EEG Source Localization Using LAPPS: Least Absolute l-P (0 < p < 1) Penalized Solution

A deep learning framework leveraging spatiotemporal feature fusion for electrophysiological source imaging

BACKGROUND AND OBJECTIVES

Electrophysiological source imaging (ESI) is a challenging technique for noninvasively measuring brain activity, which involves solving a highly ill-posed inverse problem. Traditional methods attempt to address this challenge by imposing various priors, but considering the complexity and dynamic nature of the brain activity, these priors may not accurately reflect the true attributes of brain sources. In this study, we propose a novel deep learning-based framework, spatiotemporal source imaging network (SSINet), designed to provide accurate spatiotemporal estimates of brain activity using electroencephalography (EEG).

METHODS

SSINet integrates a residual network (ResBlock) for spatial feature extraction and a bidirectional LSTM for capturing temporal dynamics, fused through a Transformer module to capture global dependencies. A channel attention mechanism is employed to prioritize active brain regions, improving both the accuracy of the model and its interpretability. Additionally, a weighted loss function is introduced to address the spatial sparsity of the brain activity.

RESULTS

We evaluated the performance of SSINet through numerical simulations and found that it outperformed several state-of-the-art ESI methods across various conditions, such as varying numbers of sources, source range, and signal-to-noise ratio levels. Furthermore, SSINet demonstrated robust performance even with electrode position offsets and changes in conductivity. We also validated the model on three real EEG datasets: visual, auditory, and somatosensory stimuli. The results show that the source activity reconstructed by SSINet aligns closely with the established physiological basis of brain function.

CONCLUSIONS

SSINet provides accurate and stable source imaging results.

XDL-ESI: Electrophysiological Sources Imaging via explainable deep learning framework with validation on simultaneous EEG and iEEG

Electroencephalography (EEG) or Magnetoencephalography (MEG) source imaging aims to estimate the underlying activated brain sources to explain the observed EEG/MEG recordings. Solving the inverse problem of EEG/MEG Source Imaging (ESI) is challenging due to its ill-posed nature. To achieve a unique solution, it is essential to apply sophisticated regularization constraints to restrict the solution space. Traditionally, the design of regularization terms is based on assumptions about the spatiotemporal structure of the underlying source dynamics. In this paper, we propose a novel paradigm for ESI via an Explainable Deep Learning framework, termed as XDL-ESI, which connects the iterative optimization algorithm with deep learning architecture by unfolding the iterative updates with neural network modules. The proposed framework has the advantages of (1) establishing a data-driven approach to model the source solution structure instead of using hand-crafted regularization terms; (2) improving the robustness of source solutions by introducing a topological loss that leverages the geometric spatial information applying varying penalties on distinct localization errors; (3) improving the reconstruction efficiency and interpretability as it inherits the advantages from both the iterative optimization algorithms (interpretability) and deep learning approaches (function approximation). The proposed XDL-ESI framework provides an efficient, accurate, and interpretable paradigm to solve the ESI inverse problem with satisfactory performance in both simulated data and real clinical data. Specially, this approach is further validated using simultaneous EEG and intracranial EEG (iEEG).

EEG dynamic source imaging using a regularized optimization with spatio-temporal constraints

One of the most important needs in neuroimaging is brain dynamic source imaging with high spatial and temporal resolution. EEG source imaging estimates the underlying sources from EEG recordings, which provides enhanced spatial resolution with intrinsically high temporal resolution. To ensure identifiability in the underdetermined source reconstruction problem, constraints on EEG sources are essential. This paper introduces a novel method for estimating source activities based on spatio-temporal constraints and a dynamic source imaging algorithm. The method enhances time resolution by incorporating temporal evolution of neural activity into a regularization function. Additionally, two spatial regularization constraints based on L 1 and L 2 norms are applied in the transformed domain to address both focal and spread neural activities, achieved through spatial gradient and Laplacian transform. Performance evaluation, conducted quantitatively using synthetic datasets, discusses the influence of parameters such as source extent, number of sources, correlation level, and SNR level on temporal and spatial metrics. Results demonstrate that the proposed method provides superior spatial and temporal reconstructions compared to state-of-the-art inverse solutions including STRAPS, sLORETA, SBL, dSPM, and MxNE. This improvement is attributed to the simultaneous integration of transformed spatial and temporal constraints. When applied to a real auditory ERP dataset, our algorithm accurately reconstructs brain source time series and locations, effectively identifying the origins of auditory evoked potentials. In conclusion, our proposed method with spatio-temporal constraints outperforms the state-of-the-art algorithms in estimating source distribution and time courses.

Effect of Inverse Solutions, Connectivity Measures, and Node Sizes on EEG Source Network: A Simultaneous EEG Study

Brain network provides an essential perspective for studying normal and pathological brain activities. Reconstructing the brain network in the source space becomes more needed, for example, as a target in non-invasive neuromodulation. Precise estimating source activities from the scalp EEG is still challenging because it is an ill-posed question and because of the volume conduction effect. There is no consensus on how to reconstruct the EEG source network. This study uses simultaneous scalp EEG and stereo-EEG to investigate the effect of inverse solutions, connectivity measures, and node sizes on the reconstruction of the source network. We evaluated the performance of different methods on both source activity and network. Numerical simulation was also carried out for comparison. The weighted phase-lag index (wPLI) method achieved significantly better performance on the reconstructed networks in source space than five other connectivity measures (directed transfer function (DTF), partial directed coherence (PDC), efficient effective connectivity (EEC), Pearson correlation coefficient (PCC), and amplitude envelope correlation (AEC)). There is no significant difference between the inverse solutions (standardized low-resolution brain electromagnetic tomography (sLORETA), weighted minimum norm estimate (wMNE), and linearly constrained minimum variance (LCMV) beamforming) on the reconstructed source networks. The source network based on signal phases can fit intracranial activities better than signal waveform properties or causality. Our study provides a basis for reconstructing source space networks from scalp EEG, especially for future neuromodulation research.

Multi-Modal Electrophysiological Source Imaging With Attention Neural Networks Based on Deep Fusion of EEG and MEG

The process of reconstructing underlying cortical and subcortical electrical activities from Electroencephalography (EEG) or Magnetoencephalography (MEG) recordings is called Electrophysiological Source Imaging (ESI). Given the complementarity between EEG and MEG in measuring radial and tangential cortical sources, combined EEG/MEG is considered beneficial in improving the reconstruction performance of ESI algorithms. Traditional algorithms mainly emphasize incorporating predesigned neurophysiological priors to solve the ESI problem. Deep learning frameworks aim to directly learn the mapping from scalp EEG/MEG measurements to the underlying brain source activities in a data-driven manner, demonstrating superior performance compared to traditional methods. However, most of the existing deep learning approaches for the ESI problem are performed on a single modality of EEG or MEG, meaning the complementarity of these two modalities has not been fully utilized. How to fuse the EEG and MEG in a more principled manner under the deep learning paradigm remains a challenging question. This study develops a Multi-Modal Deep Fusion (MMDF) framework using Attention Neural Networks (ANN) to fully leverage the complementary information between EEG and MEG for solving the ESI inverse problem, which is termed as MMDF-ANN. Specifically, our proposed brain source imaging approach consists of four phases, including feature extraction, weight generation, deep feature fusion, and source mapping. Our experimental results on both synthetic dataset and real dataset demonstrated that using a fusion of EEG and MEG can significantly improve the source localization accuracy compared to using a single-modality of EEG or MEG. Compared to the benchmark algorithms, MMDF-ANN demonstrated good stability when reconstructing sources with extended activation areas and situations of EEG/MEG measurements with a low signal-to-noise ratio.

Verification of Source Activations in a 3D Brain Model Using 'CLEVER' Algorithm for Mental Arithmetic Conditions

Background: Living conditions are becoming challenging day by day. Mental stress on individuals is increasing due to multiple reasons. As mental stress is a major cause of mental illness, it must be detected at the earliest to prevent serious conditions such as depression and anxiety.

PURPOSE

The focus of this study is to detect the exact location of the source which causes such damage. In this article, we analyse the mental conditions of subjects under a workload of performing mental arithmetic calculations for various frequency bands and plot the topography to understand the areas of active potentials.

METHODS

We propose a Novel Cluster Ensemble Verifier (CLEVER) algorithm, which combines two different techniques: clustering and source localisation. The proposed algorithm is highly efficient in identifying the exact location of the source. It is seen that the topographic plots of the independent component analysis (ICA), which has the maximum percentage of relative variance, correlates to the cluster generated. We are able to give the percentage-wise contribution of every component which is responsible for brain source activation with less time complexity.

RESULTS

Out of 72 subjects, in 67 subjects, 299 out of 433 components originate from the occipital and parietal areas of the brain with a maximum power of 43.5 µv2. As an example, the relative variance of one component is found to be contributing up to 74.03% to source activations. Clusters show similarity across the subjects in the parietal and occipital areas of the brain. The dataset used for experimentation is EEGMAT from Physionet's repository. The computation time for the algorithms is 17.6 ± 3.2 minutes. Conclusion: Findings show that during mental arithmetic calculations, both occipital and parietal areas of the brain are involved. As the data is acquired by orally mentioning the mathematical problem, subjects tend to visualise the numbers while finding the solution, which is reflected in the occipital area of the brain. CLEVER algorithm verifies the origin of the activity in the occipital and parietal areas of the brain.

Rejuvenating classical brain electrophysiology source localization methods with spatial graph Fourier filters for source extents estimation

EEG/MEG source imaging (ESI) aims to find the underlying brain sources to explain the observed EEG or MEG measurement. Multiple classical approaches have been proposed to solve the ESI problem based on different neurophysiological assumptions. To support clinical decision-making, it is important to estimate not only the exact location of the source signal but also the extended source activation regions. Existing methods may render over-diffuse or sparse solutions, which limit the source extent estimation accuracy. In this work, we leverage the graph structures defined in the 3D mesh of the brain and the spatial graph Fourier transform (GFT) to decompose the spatial graph structure into sub-spaces of low-, medium-, and high-frequency basis. We propose to use the low-frequency basis of spatial graph filters to approximate the extended areas of brain activation and embed the GFT into the classical ESI methods. We validated the classical source localization methods with the corresponding improved version using GFT in both synthetic data and real data. We found the proposed method can effectively reconstruct focal source patterns and significantly improve the performance compared to the classical algorithms.

μ-STAR: A novel framework for spatio-temporal M/EEG source imaging optimized by microstates

Source imaging of Electroencephalography (EEG) and Magnetoencephalography (MEG) provides a noninvasive way of monitoring brain activities with high spatial and temporal resolution. In order to address this highly ill-posed problem, conventional source imaging models adopted spatio-temporal constraints that assume spatial stability of the source activities, neglecting the transient characteristics of M/EEG. In this work, a novel source imaging method μ-STAR that includes a microstate analysis and a spatio-temporal Bayesian model was introduced to address this problem. Specifically, the microstate analysis was applied to achieve automatic determination of time window length with quasi-stable source activity pattern for optimal reconstruction of source dynamics. Then a user-specific spatial prior and data-driven temporal basis functions were utilized to characterize the spatio-temporal information of sources within each state. The solution of the source reconstruction was obtained through a computationally efficient algorithm based upon variational Bayesian and convex analysis. The performance of the μ-STAR was first assessed through numerical simulations, where we found that the determination and inclusion of optimal temporal length in the spatio-temporal prior significantly improved the performance of source reconstruction. More importantly, the μ-STAR model achieved robust performance under various settings (i.e., source numbers/areas, SNR levels, and source depth) with fast convergence speed compared with five widely-used benchmark models (including wMNE, STV, SBL, BESTIES, & SI-STBF). Additional validations on real data were then performed on two publicly-available datasets (including block-design face-processing ERP and continuous resting-state EEG). The reconstructed source activities exhibited spatial and temporal neurophysiologically plausible results consistent with previously-revealed neural substrates, thereby further proving the feasibility of the μ-STAR model for source imaging in various applications.

WRA-MTSI: A Robust Extended Source Imaging Algorithm Based on Multi-Trial EEG

OBJECTIVE

Reconstructing brain activities from electroencephalography (EEG) signals is crucial for studying brain functions and their abnormalities. However, since EEG signals are nonstationary and vulnerable to noise, brain activities reconstructed from single-trial EEG data are often unstable, and significant variability may occur across different EEG trials even for the same cognitive task.

METHODS

In an effort to leverage the shared information across the EEG data of multiple trials, this paper proposes a multi-trial EEG source imaging method based on Wasserstein regularization, termed WRA-MTSI. In WRA-MTSI, Wasserstein regularization is employed to perform multi-trial source distribution similarity learning, and the structured sparsity constraint is enforced to enable accurate estimation of the source extents, locations and time series. The resulting optimization problem is solved by a computationally efficient algorithm based on the alternating direction method of multipliers (ADMM).

RESULTS

Both numerical simulations and real EEG data analysis demonstrate that WRA-MTSI outperforms existing single-trial ESI methods (e.g., wMNE, LORETA, SISSY, and SBL) in mitigating the influence of artifacts in EEG data. Moreover, WRA-MTSI yields superior performance compared to other state-of-the-art multi-trial ESI methods (e.g., group lasso, the dirty model, and MTW) in estimating source extents.

CONCLUSION AND SIGNIFICANCE

WRA-MTSI may serve as an effective robust EEG source imaging method in the presence of multi-trial noisy EEG data.

A Novel Method for Constructing EEG Large-Scale Cortical Dynamical Functional Network Connectivity (dFNC): WTCS

As a kind of biological network, the brain network conduces to understanding the mystery of high-efficiency information processing in the brain, which will provide instructions to develop efficient brain-like neural networks. Large-scale dynamical functional network connectivity (dFNC) provides a more context-sensitive, dynamical, and straightforward sight at a higher network level. Nevertheless, dFNC analysis needs good enough resolution in both temporal and spatial domains, and the construction of dFNC needs to capture the time-varying correlations between two multivariate time series with unmatched spatial dimensions. Effective methods still lack. With well-developed source imaging techniques, electroencephalogram (EEG) has the potential to possess both high temporal and spatial resolutions. Therefore, we proposed to construct the EEG large-scale cortical dFNC based on brain atlas to probe the subtle dynamic activities in the brain and developed a novel method, that is, wavelet coherence-S estimator (WTCS), to assess the dynamic couplings among functional subnetworks with different spatial dimensions. The simulation study demonstrated its robustness and availability of applying to dFNC. The application in real EEG data revealed the appealing "Primary peak" and "P3-like peak" in dFNC network properties and meaningful evolutions in dFNC network topology for P300. Our study brings new insights for probing brain activities at a more dynamical and higher hierarchical level and pushing forward the development of brain-inspired artificial neural networks. The proposed WTCS not only benefits the dFNC studies but also gives a new solution to capture the time-varying couplings between the multivariate time series that is often encountered in signal processing disciplines.

Visual Selective Attention P300 Source in Frontal-Parietal Lobe: ERP and fMRI Study

Visual selective attention can be achieved into bottom-up and top-down attention. Different selective attention tasks involve different attention control ways. The pop-out task requires more bottom-up attention, whereas the search task involves more top-down attention. P300, which is the positive potential generated by the brain in the latency of 300 ~ 600 ms after stimulus, reflects the processing of attention. There is no consensus on the P300 source. The aim of present study is to study the source of P300 elicited by different visual selective attention. We collected thirteen participants' P300 elicited by pop-out and search tasks with event-related potentials (ERP). We collected twenty-six participants' activation brain regions in pop-out and search tasks with functional magnetic resonance imaging (fMRI). And we analyzed the sources of P300 using the ERP and fMRI integration with high temporal resolution and high spatial resolution. ERP results indicated that the pop-out task induced larger P300 than the search task. P300 induced by the two tasks distributed at frontal and parietal lobes, with P300 induced by the pop-out task mainly at the parietal lobe and that induced by the search task mainly at the frontal lobe. Further ERP and fMRI integration analysis showed that neural difference sources of P300 were the right precentral gyrus, left superior frontal gyrus (medial orbital), left middle temporal gyrus, left rolandic operculum, right postcentral gyrus, and left angular gyrus. Our study suggests that the frontal and parietal lobes contribute to the P300 component of visual selective attention.

Constructing Time-varying Directed EEG network by Multivariate Nonparametric Dynamical Granger Causality

Time-varying directed electroencephalography (EEG) network is the potential tool for studying the dynamical causality among brain areas at a millisecond level; which conduces to understanding how our brain effectively adapts to information processing, giving inspiration to causality- and brain-inspired machine learning. Currently, its construction still mainly relies on the parametric approach such as multivariate adaptive autoregressive (MVAAR), represented by the most widely used adaptive directed transfer function (ADTF). Restricted by the model assumption, the corresponding performance largely depends on the MVAAR modeling which usually encounters difficulty in fitting complex spectral features. In this study, we proposed to construct EEG directed network with multivariate nonparametric dynamical Granger causality (mndGC) method that infers the causality of a network, instead, in a data-driven way directly and therefore avoids the trap in the model-dependent parametric approach. Comparisons between mndGC and ADTF were conducted both with simulation and real data application. Simulation study demonstrated the superiority of mndGC both in noise resistance and capturing the instantaneous directed network changes. When applying to the real motor imagery (MI) data set, distinguishable network characters between left- and right-hand MI during different MI stages were better revealed by mndGC. Our study extends the nonparametric causality exploration and provides practical suggestions for the time-varying directed EEG network analysis.

A Long Short-Term Memory Network for Sparse Spatiotemporal EEG Source Imaging

EEG inverse problem is underdetermined, which poses a long standing challenge in Neuroimaging. The combination of source-imaging and analysis of cortical directional networks enables us to noninvasively explore the underlying neural processes. However, existing EEG source imaging approaches mainly focus on performing the direct inverse operation for source estimation, which will be inevitably influenced by noise and the strategy used to find the inverse solution. Here, we develop a new source imaging technique, Deep Brain Neural Network (DeepBraiNNet), for robust sparse spatiotemporal EEG source estimation. In DeepBraiNNet, considering that Recurrent Neural Network (RNN) are usually "deep" in temporal dimension and thus suitable for time sequence modelling, the RNN with Long Short-Term Memory (LSTM) is utilized to approximate the inverse operation for the lead field matrix instead of performing the direct inverse operation, which avoids the possible effect of the direct inverse operation on the underdetermined lead field matrix prone to be influenced by noise. Simulations on various source patterns and noise conditions confirmed that the proposed approach could actually recover the spatiotemporal sources well, outperforming existing state of-the-art methods. DeepBraiNNet also estimated sparse MI related activation patterns when it was applied to a real Motor Imagery dataset, consistent with other findings based on EEG and fMRI. Based on the spatiotemporal sources estimated from DeepBraiNNet, we constructed MI related cortical neural networks, which clearly exhibited strong contralateral network patterns for the two MI tasks. Consequently, DeepBraiNNet may provide an alternative way different from the conventional approaches for spatiotemporal EEG source imaging.

Sparse Granger Causality Analysis Model Based on Sensors Correlation for Emotion Recognition Classification in Electroencephalography

In recent years, affective computing based on electroencephalogram (EEG) data has attracted increased attention. As a classic EEG feature extraction model, Granger causality analysis has been widely used in emotion classification models, which construct a brain network by calculating the causal relationships between EEG sensors and select the key EEG features. Traditional EEG Granger causality analysis uses the L₂ norm to extract features from the data, and so the results are susceptible to EEG artifacts. Recently, several researchers have proposed Granger causality analysis models based on the least absolute shrinkage and selection operator (LASSO) and the L_1/2 norm to solve this problem. However, the conventional sparse Granger causality analysis model assumes that the connections between each sensor have the same prior probability. This paper shows that if the correlation between the EEG data from each sensor can be added to the Granger causality network as prior knowledge, the EEG feature selection ability and emotional classification ability of the sparse Granger causality model can be enhanced. Based on this idea, we propose a new emotional computing model, named the sparse Granger causality analysis model based on sensor correlation (SC-SGA). SC-SGA integrates the correlation between sensors as prior knowledge into the Granger causality analysis based on the L_1/2 norm framework for feature extraction, and uses L₂ norm logistic regression as the emotional classification algorithm. We report the results of experiments using two real EEG emotion datasets. These results demonstrate that the emotion classification accuracy of the SC-SGA model is better than that of existing models by 2.46–21.81%.

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.

A Novel Bayesian Approach for EEG Source Localization

We propose a new method for EEG source localization. An efficient solution to this problem requires choosing an appropriate regularization term in order to constraint the original problem. In our work, we adopt the Bayesian framework to place constraints; hence, the regularization term is closely connected to the prior distribution. More specifically, we propose a new sparse prior for the localization of EEG sources. The proposed prior distribution has sparse properties favoring focal EEG sources. In order to obtain an efficient algorithm, we use the variational Bayesian (VB) framework which provides us with a tractable iterative algorithm of closed-form equations. Additionally, we provide extensions of our method in cases where we observe group structures and spatially extended EEG sources. We have performed experiments using synthetic EEG data and real EEG data from three publicly available datasets. The real EEG data are produced due to the presentation of auditory and visual stimulus. We compare the proposed method with well-known approaches of EEG source localization and the results have shown that our method presents state-of-the-art performance, especially in cases where we expect few activated brain regions. The proposed method can effectively detect EEG sources in various circumstances. Overall, the proposed sparse prior for EEG source localization results in more accurate localization of EEG sources than state-of-the-art approaches.