Lp norm iterative sparse solution for EEG source Localization

Accuracy of SEEG Source Localization: A Pilot Study Using Corticocortical Evoked Potentials

INTRODUCTION

EEG source localization is an established technique for localizing scalp EEG in medically refractory epilepsy but has not been adequately studied with intracranial EEG (iEEG). Differences in sensor location and spatial sampling may affect the accuracy of EEG source localization with iEEG. Corticocortical evoked potentials can be used to evaluate EEG source localization algorithms for iEEG given the known source location.

METHODS

We recorded 205 sets of corticocortical evoked potentials using low-frequency single-pulse electrical stimulation in four patients with iEEG. Averaged corticocortical evoked potentials were analyzed using 11 distributed source algorithms and compared using the Wilcoxon signed-rank test ( P < 0.05). We measured the localization error from stimulated electrodes and the spatial dispersion of each solution.

RESULTS

Minimum norm, standard low-resolution electromagnetic tomography (sLORETA), LP Norm, sLORETA-weighted accurate minimum norm (SWARM), exact LORETA (eLORETA), standardized weighted LORETA (swLORETA), and standardized shrinking LORETA-FOCUSS (ssLOFO) had the least localization error (13.3-15.7 mm) and were superior to focal underdetermined system solver (FOCUSS), logistic autoregressive average (LAURA, and LORETA, 17.9-21.7, P < 0.001). The FOCUSS solution had the smallest spatial dispersion (7.4 mm), followed by minimum norm, L1 norm, LP norm, and SWARM (20.8-28.3 mm). Gray matter stimulations had less localization error than white matter (median differences 3.1-6.1 mm) across all algorithms except SWARM, LORETA, and logistic autoregressive average. A multivariate linear regression showed that distance from the source to sensors and gray/white matter stimulation had a significant effect on localization error for some algorithms but not SWARM, minimum norm, focal underdetermined system solver, logistic autoregressive average, and LORETA.

CONCLUSIONS

Our study demonstrated that minimum norm, L1 norm, LP norm, and SWARM localize iEEG corticocortical evoked potentials well with lower localization error and spatial dispersion. Larger studies are needed to confirm these findings.

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).

Electromagnetic Source Imaging via a Data-Synthesis-Based Convolutional Encoder-Decoder Network

Electromagnetic source imaging (ESI) requires solving a highly ill-posed inverse problem. To seek a unique solution, traditional ESI methods impose various forms of priors that may not accurately reflect the actual source properties, which may hinder their broad applications. To overcome this limitation, in this article, a novel data-synthesized spatiotemporally convolutional encoder-decoder network (DST-CedNet) method is proposed for ESI. The DST-CedNet recasts ESI as a machine learning problem, where discriminative learning and latent-space representations are integrated in a CedNet to learn a robust mapping from the measured electroencephalography/magnetoencephalography (E/MEG) signals to the brain activity. In particular, by incorporating prior knowledge regarding dynamical brain activities, a novel data synthesis strategy is devised to generate large-scale samples for effectively training CedNet. This stands in contrast to traditional ESI methods where the prior information is often enforced via constraints primarily aimed for mathematical convenience. Extensive numerical experiments as well as analysis of a real MEG and epilepsy EEG dataset demonstrate that the DST-CedNet outperforms several state-of-the-art ESI methods in robustly estimating source signals under a variety of source configurations.

Integration of Simultaneous fMRI and EEG source localization in emotional decision problems

Simultaneous EEG-fMRI has been a powerful technique to understand the mechanism of the brain in recent years. In this paper, we develop an integrating method by integrating the EEG data into the fMRI data based on the parametric empirical Bayesian (PEB) model to improve the accuracy of the brain source location. The gambling task, a classic paradigm, is used for the emotional decision-making study in this paper. The proposed method was conducted on 21 participants, including 16 men and 5 women. Contrary to the previous method that only localizes the area widely distributed across the ventral striatum and orbitofrontal cortex, the proposed method localizes accurately at the orbital frontal cortex during the process of the brain's emotional decision-making. The activated brain regions extracted by source localization were mainly located in the prefrontal and orbitofrontal lobes; the activation of the temporal pole regions unrelated to reward processing disappeared, and the activation of the somatosensory cortex and motor cortex was significantly reduced. The log evidence shows that the integration of simultaneous fMRI and EEG method based on synchronized data evidence is 22420, the largest value among the three methods. The integration method always takes on a larger value of log evidence and describes a better performance in analysis associated with source localization. DATA AVAILABILITY: The data used in the current study are available from the corresponding authouponon reasonable request.

Automatic depth map retrieval from digital holograms using a depth-from-focus approach

Recovering the scene depth map from a computer-generated hologram is a problem that remains unsolved, despite the growing interest in the subject. In this paper, we propose to study the application of depth-from-focus (DFF) methods to retrieve the depth information from the hologram. We discuss the different hyperparameters that are required for the application of the method and their impact on the final result. The obtained results show that DFF methods can be used for depth estimation from the hologram if the set of hyperparameters is well chosen.

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 algorithms for EEG source localization

Source localization using EEG is important in diagnosing various physiological and psychiatric diseases related to the brain. The high temporal resolution of EEG helps medical professionals assess the internal physiology of the brain in a more informative way. The internal sources are obtained from EEG by an inversion process. The number of sources in the brain outnumbers the number of measurements. In this article, a comprehensive review of the state-of-the-art sparse source localization methods in this field is presented. A recently developed method, certainty-based-reduced-sparse-solution (CARSS), is implemented and is examined. A vast comparative study is performed using a sixty-four-channel setup involving two source spaces. The first source space has 5004 sources and the other has 2004 sources. Four test cases with one, three, five, and seven simulated active sources are considered. Two noise levels are also being added to the noiseless data. The CARSS is also evaluated. The results are examined. A real EEG study is also attempted. Graphical Abstract.

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%.

High-Resolution EEG Source Localization in Segmentation-Free Head Models Based on Finite-Difference Method and Matching Pursuit Algorithm

Electroencephalogram (EEG) is a method to monitor electrophysiological activity on the scalp, which represents the macroscopic activity of the brain. However, it is challenging to identify EEG source regions inside the brain based on data measured by a scalp-attached network of electrodes. The accuracy of EEG source localization significantly depends on the type of head modeling and inverse problem solver. In this study, we adopted different models with a resolution of 0.5 mm to account for thin tissues/fluids, such as the cerebrospinal fluid (CSF) and dura. In particular, a spatially dependent conductivity (segmentation-free) model created using deep learning was developed and used for more realist representation of electrical conductivity. We then adopted a multi-grid-based finite-difference method (FDM) for forward problem analysis and a sparse-based algorithm to solve the inverse problem. This enabled us to perform efficient source localization using high-resolution model with a reasonable computational cost. Results indicated that the abrupt spatial change in conductivity, inherent in conventional segmentation-based head models, may trigger source localization error accumulation. The accurate modeling of the CSF, whose conductivity is the highest in the head, was an important factor affecting localization accuracy. Moreover, computational experiments with different noise levels and electrode setups demonstrate the robustness of the proposed method with segmentation-free head model.

ECG Localization Method Based on Volume Conductor Model and Kalman Filtering

The 12-lead electrocardiogram was invented more than 100 years ago and is still used as an essential tool in the early detection of heart disease. By estimating the time-varying source of the electrical activity from the potential changes, several types of heart disease can be noninvasively identified. However, most previous studies are based on signal processing, and thus an approach that includes physics modeling would be helpful for source localization problems. This study proposes a localization method for cardiac sources by combining an electrical analysis with a volume conductor model of the human body as a forward problem and a sparse reconstruction method as an inverse problem. Our formulation estimates not only the current source location but also the current direction. For a 12-lead electrocardiogram system, a sensitivity analysis of the localization to cardiac volume, tilted angle, and model inhomogeneity was evaluated. Finally, the estimated source location is corrected by Kalman filter, considering the estimated electrocardiogram source as time-sequence data. For a high signal-to-noise ratio (greater than 20 dB), the dominant error sources were the model inhomogeneity, which is mainly attributable to the high conductivity of the blood in the heart. The average localization error of the electric dipole sources in the heart was 12.6 mm, which is comparable to that in previous studies, where a less detailed anatomical structure was considered. A time-series source localization with Kalman filtering indicated that source mislocalization could be compensated, suggesting the effectiveness of the source estimation using the current direction and location simultaneously. For the electrocardiogram R-wave, the mean distance error was reduced to less than 7.3 mm using the proposed method. Considering the physical properties of the human body with Kalman filtering enables highly accurate estimation of the cardiac electric signal source location and direction. This proposal is also applicable to electrode configuration, such as ECG sensing systems.

Robust Autoregression with Exogenous Input Model for System Identification and Predicting

Autoregression with exogenous input (ARX) is a widely used model to estimate the dynamic relationships between neurophysiological signals and other physiological parameters. Nevertheless, biological signals, such as electroencephalogram (EEG), arterial blood pressure (ABP), and intracranial pressure (ICP), are inevitably contaminated by unexpected artifacts, which may distort the parameter estimation due to the use of the L2 norm structure. In this paper, we defined the ARX in the Lp (p ≤ 1) norm space with the aim of resisting outlier influence and designed a feasible iteration procedure to estimate model parameters. A quantitative evaluation with various outlier conditions demonstrated that the proposed method could estimate ARX parameters more robustly than conventional methods. Testing with the resting-state EEG with ocular artifacts demonstrated that the proposed method could predict missing data with less influence from the artifacts. In addition, the results on ICP and ABP data further verified its efficiency for model fitting and system identification. The proposed Lp-ARX may help capture system parameters reliably with various input and output signals that are contaminated with artifacts.

Improvement in EEG Source Imaging Accuracy by Means of Wavelet Packet Transform and Subspace Component Selection

The electroencephalograph (EEG) source imaging (ESI) method is a non-invasive method that provides high temporal resolution imaging of brain electrical activity on the cortex. However, because the accuracy of EEG source imaging is often affected by unwanted signals such as noise or other source-irrelevant signals, the results of ESI are often incongruous with the real sources of brain activities. This study presents a novel ESI method (WPESI) that is based on wavelet packet transform (WPT) and subspace component selection to image the cerebral activities of EEG signals on the cortex. First, the original EEG signals are decomposed into several subspace components by WPT. Second, the subspaces associated with brain sources are selected and the relevant signals are reconstructed by WPT. Finally, the current density distribution in the cerebral cortex is obtained by establishing a boundary element model (BEM) from head MRI and applying the appropriate inverse calculation. In this study, the localization results obtained by this proposed approach were better than those of the original sLORETA approach (OESI) in the computer simulations and visual evoked potential (VEP) experiments. For epilepsy patients, the activity sources estimated by this proposed algorithm conformed to the seizure onset zones. The WPESI approach is easy to implement achieved favorable accuracy in terms of EEG source imaging. This demonstrates the potential for use of the WPESI algorithm to localize epileptogenic foci from scalp EEG signals.

Efficient high resolution sLORETA in brain source localization

Objective. Estimation of the source location within the brain from electroencephalography (EEG) and magnetoencephalography measures is a challenging task. Among the existing techniques in the field, which are known as brain imaging methods, standardized low-resolution brain electromagnetic tomography (sLORETA) is the most popular method due to its simplicity and high accuracy. However, in this work we illustrate that sLORETA is still noisy and the additive noise is causing the blurry image. The existing pre-fixed/manual thresholding process after sLORETA can partially take care of denoising. However, this ad-hoc theresholding can either remove so much of the desired data or leave much of the noise in the process. Manual correction to avoid such extreme cases can be time-consuming. The objective of this paper is to automate the denoising process in the form of adaptive thresholding. Approach. The proposed method, denoted by efficient high-resolution sLORETA (EHR-sLORETA), is based on minimizing the error between the desired denoised source and the source estimates. Main results. The approach is evaluated using synthetic EEG and real EEG data. spatial dispersion (SD), and mean square error (MSE) are used as metrics to provide the quantitative performance of the method. In addition, qualitative analysis of the method is provided for real EEG data. This proposed model demonstrates advantages over the existing methods in sense of accuracy and robustness with SD and MSE comparison. Significance. EHR-sLORETA could have a significant impact on clinical studies with source estimation task, as it improves the accuracy of source estimation and eliminates the need for manual thresholding.

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.

Sparse Recovery Beyond Compressed Sensing: Separable Nonlinear Inverse Problems

Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly on certain parameters of interest. These parameters may represent neuronal activity in a human brain, frequencies of electromagnetic waves, fluorescent probes in a cell, or magnetic relaxation times of biological tissues. Separable nonlinear inverse problems can be reformulated as underdetermined sparse-recovery problems, and solved using convex programming. This approach has had empirical success in a variety of domains, from geophysics to medical imaging, but lacks a theoretical justification. In particular, compressed-sensing theory does not apply, because the measurement operators are deterministic and violate incoherence conditions such as the restricted-isometry property. Our main contribution is a theory for sparse recovery adapted to deterministic settings. We show that convex programming succeeds in recovering the parameters of interest, as long as their values are sufficiently distinct with respect to the correlation structure of the measurement operator. The theoretical results are illustrated through numerical experiments for two applications: heat-source localization and estimation of brain activity from electroencephalography data.

Directed EEG neural network analysis by LAPPS (p≤1) Penalized sparse Granger approach

The conventional multivariate Granger Analysis (GA) of directed interactions has been widely applied in brain network construction based on EEG recordings as well as fMRI. Nevertheless, EEG is usually inevitably contaminated by strong noise, which may cause network distortion due to the L2-norm used in GAs for directed network recovery. The Lp (p ≤1) norm has been shown to be more robust to outliers as compared to LASSO and L2-GAs. Motivated to construct the sparse brain networks under strong noise condition, we hereby introduce a new approach for GA analysis, termed LAPPS (Least Absolute LP (0<p<1) Penalized Solution). LAPPS utilizes the L1-loss function for the residual error to alleviate the effect of outliers, and another Lp-penalty term (p=0.5) to obtain the sparse connections while suppressing the spurious linkages in the networks. The simulation results reveal that LAPPS obtained the best performance under various noise conditions. In a real EEG data test when subjects performed the left and right hand Motor Imagery (MI) for brain network estimation, LAPPS also obtained a sparse network pattern with the hub at the contralateral brain primary motor areas consistent with the physiological basis of MI.

Certainty-Based Reduced Sparse Solution for Dense Array EEG Source Localization

The EEG source localization is an ill-posed problem. It involves estimation of the sources which outnumbers the number of measurements. For a given measurement at a given time all sources are not active this makes the problem as sparse inversion problem. This paper presents a new approach for dense array EEG source localization. This paper aims at reducing the solution space to only most certain sources and thereby reducing the problem of ill-posedness. This employs a two-stage method, where the first stage finds the most certain sources that are likely to produce the observed EEG by using a statistical measure of sources, the second stage solves the inverse problem by restricting the solution space to only most certain sources and their neighbors. This reduces the solution space for other source localization methods hence improvise their accuracy in localizing the active neurological sources in the brain. This method has been validated and applied to real 256 channel data and the results were analyzed.

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

OBJECTIVE

The electroencephalographic (EEG) inverse problem is ill-posed owing to the electromagnetism Helmholtz theorem and since there are fewer observations than the unknown variables. Apart from the strong background activities (ongoing EEG), evoked EEG is also inevitably contaminated by strong outliers caused by head movements or ocular movements during recordings.

METHODS

Considering the sparse activations during high cognitive processing, we propose a novel robust EEG source imaging algorithm, LAPPS (Least Absolute -P (0 < p < 1) Penalized Solution), which employs the -loss for the residual error to alleviate the effect of outliers and another -penalty norm (p=0.5) to obtain sparse sources while suppressing Gaussian noise in EEG recordings. The resulting optimization problem is solved using a modified ADMM algorithm.

RESULTS

Simulation study was performed to recover sparse signals of randomly selected sources using LAPPS and various methods commonly used for EEG source imaging including WMNE, -norm, sLORETA and FOCUSS solution. The simulation comparison quantitatively demonstrates that LAPPS obtained the best performances in all the conducted simulations for various dipoles configurations under various SNRs on a realistic head model. Moreover, in the localization of brain neural generators in a real visual oddball experiment, LAPPS obtained sparse activations consistent with previous findings revealed by EEG and fMRI.

CONCLUSION

This study demonstrates a potentially useful sparse method for EEG source imaging, creating a platform for investigating the brain neural generators.

SIGNIFICANCE

This method alleviates the effect of noise and recovers sparse sources while maintaining a low computational complexity due to the cheap matrix-vector multiplication.

Multicompartment Magnetic Resonance Fingerprinting

Magnetic resonance fingerprinting (MRF) is a technique for quantitative estimation of spin- relaxation parameters from magnetic-resonance data. Most current MRF approaches assume that only one tissue is present in each voxel, which neglects intravoxel structure, and may lead to artifacts in the recovered parameter maps at boundaries between tissues. In this work, we propose a multicompartment MRF model that accounts for the presence of multiple tissues per voxel. The model is fit to the data by iteratively solving a sparse linear inverse problem at each voxel, in order to express the measured magnetization signal as a linear combination of a few elements in a precomputed fingerprint dictionary. Thresholding-based methods commonly used for sparse recovery and compressed sensing do not perform well in this setting due to the high local coherence of the dictionary. Instead, we solve this challenging sparse-recovery problem by applying reweighted-𝓁1-norm regularization, implemented using an efficient interior-point method. The proposed approach is validated with simulated data at different noise levels and undersampling factors, as well as with a controlled phantom-imaging experiment on a clinical magnetic-resonance system.

Robust Granger Analysis in Lp Norm Space for Directed EEG Network Analysis

Granger analysis (GA) is widely used to construct directed brain networks based on various physiological recordings, such as functional magnetic resonance imaging, and electroencephalogram (EEG). However, in real applications, EEGs are inevitably contaminated by unexpected artifacts that may distort the networks because of the L2 norm structure utilized in GAs when estimating directed links. Compared with the L2 norm, the Lp ( ) norm can compress outlier effects. In this paper, an extended GA is constructed by applying the Lp ( ) norm strategy to estimate robust causalities under outlier conditions, and a feasible iteration procedure is utilized to solve the new GA model. A quantitative evaluation using a predefined simulation network demonstrates smaller bias errors and higher linkage consistence for the Lp ( , 0.8, 0.6, 0.4, 0.2) -GAs compared with both the Lasso- and L2-GAs under various simulated outlier conditions. Applications in resting-state EEGs that contain ocular artifacts also show that the proposed GA can effectively compress the ocular outlier influence and recover the reliable networks. The proposed Lp-GA may be helpful in capturing the reliable network structure when EEGs are contaminated with artifacts in related studies.

Cortical Dynamic Causality Network for Auditory-Motor Tasks

Motor preparation and execution require the interactions of a large-scale brain network, while the study of the dynamic changes of their interactions could uncover the underlying neural mechanism of the corresponding information processing. This dynamic analysis requires high temporal resolution of the recorded signals. Electroencephalogram (EEG) with high temporal resolution has been widely used in related studies. However, studies based on scalp EEG always lead to distorted results, due to scalp volume conduction, compared with that of cortically recorded signals. In the current study, the dynamic networks of motor preparation and execution are investigated using Go/No-go tasks performed with the left/right hand. In the analysis, the EEG source localization and dynamic causal model are combined together to investigate the neural processes of motor preparation and execution. The results show that similar network patterns with nodes distributed in the bilateral occipital lobe, bilateral temporal lobe, bilateral dorsolateral prefrontal cortex, and contralateral supplementary motor area could be revealed for both the Go and No-go tasks. Statistical testing further indicates that stronger couplings with the supplementary motor area could be found in Go and right-hand response tasks compared with No-go and left-hand response tasks, respectively. The findings in the current study demonstrate that the information exchange within the motor related brain networks plays an important role for motor related functions, i.e., the different motor functions may have the different information exchange and processing network patterns.

The Iterative Reweighted Mixed-Norm Estimate for Spatio-Temporal MEG/EEG Source Reconstruction

Source imaging based on magnetoencephalography (MEG) and electroencephalography (EEG) allows for the non-invasive analysis of brain activity with high temporal and good spatial resolution. As the bioelectromagnetic inverse problem is ill-posed, constraints are required. For the analysis of evoked brain activity, spatial sparsity of the neuronal activation is a common assumption. It is often taken into account using convex constraints based on the l1-norm. The resulting source estimates are however biased in amplitude and often suboptimal in terms of source selection due to high correlations in the forward model. In this work, we demonstrate that an inverse solver based on a block-separable penalty with a Frobenius norm per block and a l0.5-quasinorm over blocks addresses both of these issues. For solving the resulting non-convex optimization problem, we propose the iterative reweighted Mixed Norm Estimate (irMxNE), an optimization scheme based on iterative reweighted convex surrogate optimization problems, which are solved efficiently using a block coordinate descent scheme and an active set strategy. We compare the proposed sparse imaging method to the dSPM and the RAP-MUSIC approach based on two MEG data sets. We provide empirical evidence based on simulations and analysis of MEG data that the proposed method improves on the standard Mixed Norm Estimate (MxNE) in terms of amplitude bias, support recovery, and stability.

Bayesian electromagnetic spatio-temporal imaging of extended sources with Markov Random Field and temporal basis expansion

Estimating the locations and spatial extents of brain sources poses a long-standing challenge for electroencephalography and magnetoencephalography (E/MEG) source imaging. In the present work, a novel source imaging method, Bayesian Electromagnetic Spatio-Temporal Imaging of Extended Sources (BESTIES), which is built upon a Bayesian framework that determines the spatio-temporal smoothness of source activities in a fully data-driven fashion, is proposed to address this challenge. In particular, a Markov Random Field (MRF), which can precisely capture local cortical interactions, is employed to characterize the spatial smoothness of source activities, the temporal dynamics of which are modeled by a set of temporal basis functions (TBFs). Crucially, all of the unknowns in the MRF and TBF models are learned from the data. To accomplish model inference efficiently on high-resolution source spaces, a scalable algorithm is developed to approximate the posterior distribution of the source activities, which is based on the variational Bayesian inference and convex analysis. The performance of BESTIES is assessed using both simulated and actual human E/MEG data. Compared with L₂-norm constrained methods, BESTIES is superior in reconstructing extended sources with less spatial diffusion and less localization error. By virtue of the MRF, BESTIES also overcomes the drawback of over-focal estimates in sparse constrained methods.

Sparse Bayesian Learning for Obtaining Sparsity of EEG Frequency Bands Based Feature Vectors in Motor Imagery Classification

Effective common spatial pattern (CSP) feature extraction for motor imagery (MI) electroencephalogram (EEG) recordings usually depends on the filter band selection to a large extent. Subband optimization has been suggested to enhance classification accuracy of MI. Accordingly, this study introduces a new method that implements sparse Bayesian learning of frequency bands (named SBLFB) from EEG for MI classification. CSP features are extracted on a set of signals that are generated by a filter bank with multiple overlapping subbands from raw EEG data. Sparse Bayesian learning is then exploited to implement selection of significant features with a linear discriminant criterion for classification. The effectiveness of SBLFB is demonstrated on the BCI Competition IV IIb dataset, in comparison with several other competing methods. Experimental results indicate that the SBLFB method is promising for development of an effective classifier to improve MI classification.

Incorporating priors for EEG source imaging and connectivity analysis

Electroencephalography source imaging (ESI) is a useful technique to localize the generators from a given scalp electric measurement and to investigate the temporal dynamics of the large-scale neural circuits. By introducing reasonable priors from other modalities, ESI reveals the most probable sources and communication structures at every moment in time. Here, we review the available priors from such techniques as magnetic resonance imaging (MRI), functional MRI (fMRI), and positron emission tomography (PET). The modality's specific contribution is analyzed from the perspective of source reconstruction. For spatial priors, EEG-correlated fMRI, temporally coherent networks (TCNs) and resting-state fMRI are systematically introduced in the ESI. Moreover, the fiber tracking (diffusion tensor imaging, DTI) and neuro-stimulation techniques (transcranial magnetic stimulation, TMS) are also introduced as the potential priors, which can help to draw inferences about the neuroelectric connectivity in the source space. We conclude that combining EEG source imaging with other complementary modalities is a promising approach toward the study of brain networks in cognitive and clinical neurosciences.

Sparse EEG Source Localization Using Bernoulli Laplacian Priors

Source localization in electroencephalography has received an increasing amount of interest in the last decade. Solving the underlying ill-posed inverse problem usually requires choosing an appropriate regularization. The usual l2 norm has been considered and provides solutions with low computational complexity. However, in several situations, realistic brain activity is believed to be focused in a few focal areas. In these cases, the l2 norm is known to overestimate the activated spatial areas. One solution to this problem is to promote sparse solutions for instance based on the l1 norm that are easy to handle with optimization techniques. In this paper, we consider the use of an l0 + l1 norm to enforce sparse source activity (by ensuring the solution has few nonzero elements) while regularizing the nonzero amplitudes of the solution. More precisely, the l0 pseudonorm handles the position of the nonzero elements while the l1 norm constrains the values of their amplitudes. We use a Bernoulli-Laplace prior to introduce this combined l0 + l1 norm in a Bayesian framework. The proposed Bayesian model is shown to favor sparsity while jointly estimating the model hyperparameters using a Markov chain Monte Carlo sampling technique. We apply the model to both simulated and real EEG data, showing that the proposed method provides better results than the l2 and l1  norms regularizations in the presence of pointwise sources. A comparison with a recent method based on multiple sparse priors is also conducted.

Image reconstruction of the absorption coefficients with l 1-norm minimization from photoacoustic measurements

BACKGROUND

The photoacoustic (PA) imaging by considering light propagation into image reconstruction process can provide quantitative information of photon absorbers, such as hemoglobin and exogenous dyes, and to improve their imaging contrasts.

METHODS

A 2D image reconstruction of the distribution of the light absorption coefficient from the PA measurements with light source and ultrasound transducer placed at the identical position was tested. The PA pressures were formulated with the PA wave equation and the photon diffusion equation. The relation between the PA pressure and the absorption coefficient was linearized. The image reconstruction was carried out by minimizing the squared error between the measured and calculated PA signals. The l 1-norm of the reconstructed image was simultaneously minimized to improve the localization of the reconstructed target in the image. The image reconstruction with the l 1-norm minimization was compared to that with the Tikhonov regularization by numerical simulation and phantom experiment. In phantom experiment, an aqueous solution of the intralipid and the indocyanine green was used as the measured object. The PA probe had optical fiber for illumination and piezoelectric film for detection placed at the identical position.

RESULTS

The l 1-norm minimization reconstructed more localized target than the Tikhonov regularization.

CONCLUSIONS

The l 1-norm minimization is useful for the sparse PA image reconstruction.

Autoregressive model in the Lp norm space for EEG analysis

The autoregressive (AR) model is widely used in electroencephalogram (EEG) analyses such as waveform fitting, spectrum estimation, and system identification. In real applications, EEGs are inevitably contaminated with unexpected outlier artifacts, and this must be overcome. However, most of the current AR models are based on the L2 norm structure, which exaggerates the outlier effect due to the square property of the L2 norm. In this paper, a novel AR object function is constructed in the Lp (p≤1) norm space with the aim to compress the outlier effects on EEG analysis, and a fast iteration procedure is developed to solve this new AR model. The quantitative evaluation using simulated EEGs with outliers proves that the proposed Lp (p≤1) AR can estimate the AR parameters more robustly than the Yule-Walker, Burg and LS methods, under various simulated outlier conditions. The actual application to the resting EEG recording with ocular artifacts also demonstrates that Lp (p≤1) AR can effectively address the outliers and recover a resting EEG power spectrum that is more consistent with its physiological basis.

Reconstruction of localized fluorescent target from multi-view continuous-wave surface images of small animal with lp sparsity regularization

Fluorescence diffuse optical tomography using a multi-view continuous-wave and non-contact measurement system and an algorithm incorporating the lp (0 < p ≤ 1) sparsity regularization reconstructs a localized fluorescent target in a small animal. The measurement system provides a total of 25 fluorescence surface 2D-images of an object, which are acquired by a CCD camera from five different angles of view with excitation from five different angles. Fluorescence surface emissions from five different angles of view are simultaneously imaged on the CCD sensor, thus leading to fast acquisition of the 25 images within three minutes. The distributions of the fluorophore are reconstructed by solving the inverse problem based on the photon diffusion equations. In the reconstruction process incorporating the lp sparsity regularization, the regularization term is reformulated as a differentiable function for gradient-based non-linear optimization. Numerical simulations and phantom experiments show that the use of the lp sparsity regularization improves the localization of the target and quantitativeness of the fluorophore concentration. A mouse experiment demonstrates that a localized fluorescent target in a mouse is successfully reconstructed.

Recognizing mild cognitive impairment based on network connectivity analysis of resting EEG with zero reference

The diagnosis of mild cognitive impairment (MCI) is very helpful for early therapeutic interventions of Alzheimer's disease (AD). MCI has been proven to be correlated with disorders in multiple brain areas. In this paper, we used information from resting brain networks at different EEG frequency bands to reliably recognize MCI. Because EEG network analysis is influenced by the reference that is used, we also evaluate the effect of the reference choices on the resting scalp EEG network-based MCI differentiation. The conducted study reveals two aspects: (1) the network-based MCI differentiation is superior to the previously reported classification that uses coherence in the EEG; and (2) the used EEG reference influences the differentiation performance, and the zero approximation technique (reference electrode standardization technique, REST) can construct a more accurate scalp EEG network, which results in a higher differentiation accuracy for MCI. This study indicates that the resting scalp EEG-based network analysis could be valuable for MCI recognition in the future.

Simultaneous EEG-fMRI: trial level spatio-temporal fusion for hierarchically reliable information discovery

Simultaneous electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) have been pursued in an effort to integrate complementary noninvasive information on brain activity. The primary goal involves better information discovery of the event-related neural activations at a spatial region of the BOLD fluctuation with the temporal resolution of the electrical signal. Many techniques and algorithms have been developed to integrate EEGs and fMRIs; however, the relative reliability of the integrated information is unclear. In this work, we propose a hierarchical framework to ensure the relative reliability of the integrated results and attempt to understand brain activation using this hierarchical ideal. First, spatial Independent Component Analysis (ICA) of fMRI and temporal ICA of EEG were performed to extract features at the trial level. Second, the maximal information coefficient (MIC) was adopted to temporally match them across the modalities for both linear and non-linear associations. Third, fMRI-constrained EEG source imaging was utilized to spatially match components across modalities. The simultaneously occurring events in the above two match steps provided EEG-fMRI spatial-temporal reliable integrated information, resulting in the most reliable components with high spatial and temporal resolution information. The other components discovered in the second or third steps provided second-level complementary information for flexible and cautious explanations. This paper contains two simulations and an example of real data, and the results indicate that the framework is a feasible approach to reveal cognitive processing in the human brain.

EEG extended source localization: tensor-based vs. conventional methods

The localization of brain sources based on EEG measurements is a topic that has attracted a lot of attention in the last decades and many different source localization algorithms have been proposed. However, their performance is limited in the case of several simultaneously active brain regions and low signal-to-noise ratios. To overcome these problems, tensor-based preprocessing can be applied, which consists in constructing a space-time-frequency (STF) or space-time-wave-vector (STWV) tensor and decomposing it using the Canonical Polyadic (CP) decomposition. In this paper, we present a new algorithm for the accurate localization of extended sources based on the results of the tensor decomposition. Furthermore, we conduct a detailed study of the tensor-based preprocessing methods, including an analysis of their theoretical foundation, their computational complexity, and their performance for realistic simulated data in comparison to conventional source localization algorithms such as sLORETA, cortical LORETA (cLORETA), and 4-ExSo-MUSIC. Our objective consists, on the one hand, in demonstrating the gain in performance that can be achieved by tensor-based preprocessing, and, on the other hand, in pointing out the limits and drawbacks of this method. Finally, we validate the STF and STWV techniques on real measurements to demonstrate their usefulness for practical applications.

A review of EEG and MEG for brainnetome research

The majority of brain activities are performed by functionally integrating separate regions of the brain. Therefore, the synchronous operation of the brain's multiple regions or neuronal assemblies can be represented as a network with nodes that are interconnected by links. Because of the complexity of brain interactions and their varying effects at different levels of complexity, one of the corresponding authors of this paper recently proposed the brainnetome as a new -ome to explore and integrate the brain network at different scales. Because electroencephalography (EEG) and magnetoencephalography (MEG) are noninvasive and have outstanding temporal resolution and because they are the primary clinical techniques used to capture the dynamics of neuronal connections, they lend themselves to the analysis of the neural networks comprising the brainnetome. Because of EEG/MEG's applicability to brainnetome analyses, the aim of this review is to identify the procedures that can be used to form a network using EEG/MEG data in sensor or source space and to promote EEG/MEG network analysis for either neuroscience or clinical applications. To accomplish this aim, we show the relationship of the brainnetome to brain networks at the macroscale and provide a systematic review of network construction using EEG and MEG. Some potential applications of the EEG/MEG brainnetome are to use newly developed methods to associate the properties of a brainnetome with indices of cognition or disease conditions. Associations based on EEG/MEG brainnetome analysis may improve the comprehension of the functioning of the brain in neuroscience research or the recognition of abnormal patterns in neurological disease.

L1 norm based common spatial patterns decomposition for scalp EEG BCI

BACKGROUND

Brain computer interfaces (BCI) is one of the most popular branches in biomedical engineering. It aims at constructing a communication between the disabled persons and the auxiliary equipments in order to improve the patients' life. In motor imagery (MI) based BCI, one of the popular feature extraction strategies is Common Spatial Patterns (CSP). In practical BCI situation, scalp EEG inevitably has the outlier and artifacts introduced by ocular, head motion or the loose contact of electrodes in scalp EEG recordings. Because outlier and artifacts are usually observed with large amplitude, when CSP is solved in view of L2 norm, the effect of outlier and artifacts will be exaggerated due to the imposing of square to outliers, which will finally influence the MI based BCI performance. While L1 norm will lower the outlier effects as proved in other application fields like EEG inverse problem, face recognition, etc.

METHODS

In this paper, we present a new CSP implementation using the L1 norm technique, instead of the L2 norm, to solve the eigen problem for spatial filter estimation with aim to improve the robustness of CSP to outliers. To evaluate the performance of our method, we applied our method as well as the standard CSP and the regularized CSP with Tikhonov regularization (TR-CSP), on both the peer BCI dataset with simulated outliers and the dataset from the MI BCI system developed in our group. The McNemar test is used to investigate whether the difference among the three CSPs is of statistical significance.

RESULTS

The results of both the simulation and real BCI datasets consistently reveal that the proposed method has much higher classification accuracies than the conventional CSP and the TR-CSP.

CONCLUSIONS

By combining L1 norm based Eigen decomposition into Common Spatial Patterns, the proposed approach can effectively improve the robustness of BCI system to EEG outliers and thus be potential for the actual MI BCI application, where outliers are inevitably introduced into EEG recordings.

MEG source localization using invariance of noise space

We propose INvariance of Noise (INN) space as a novel method for source localization of magnetoencephalography (MEG) data. The method is based on the fact that modulations of source strengths across time change the energy in signal subspace but leave the noise subspace invariant. We compare INN with classical MUSIC, RAP-MUSIC, and beamformer approaches using simulated data while varying signal-to-noise ratios as well as distance and temporal correlation between two sources. We also demonstrate the utility of INN with actual auditory evoked MEG responses in eight subjects. In all cases, INN performed well, especially when the sources were closely spaced, highly correlated, or one source was considerably stronger than the other.

Group-sparse representation with dictionary learning for medical image denoising and fusion

Recently, sparse representation has attracted a lot of interest in various areas. However, the standard sparse representation does not consider the intrinsic structure, i.e., the nonzero elements occur in clusters, called group sparsity. Furthermore, there is no dictionary learning method for group sparse representation considering the geometrical structure of space spanned by atoms. In this paper, we propose a novel dictionary learning method, called Dictionary Learning with Group Sparsity and Graph Regularization (DL-GSGR). First, the geometrical structure of atoms is modeled as the graph regularization. Then, combining group sparsity and graph regularization, the DL-GSGR is presented, which is solved by alternating the group sparse coding and dictionary updating. In this way, the group coherence of learned dictionary can be enforced small enough such that any signal can be group sparse coded effectively. Finally, group sparse representation with DL-GSGR is applied to 3-D medical image denoising and image fusion. Specifically, in 3-D medical image denoising, a 3-D processing mechanism (using the similarity among nearby slices) and temporal regularization (to perverse the correlations across nearby slices) are exploited. The experimental results on 3-D image denoising and image fusion demonstrate the superiority of our proposed denoising and fusion approaches.

Integration of consonant and pitch processing as revealed by the absence of additivity in mismatch negativity

Consonants, unlike vowels, are thought to be speech specific and therefore no interactions would be expected between consonants and pitch, a basic element for musical tones. The present study used an electrophysiological approach to investigate whether, contrary to this view, there is integrative processing of consonants and pitch by measuring additivity of changes in the mismatch negativity (MMN) of evoked potentials. The MMN is elicited by discriminable variations occurring in a sequence of repetitive, homogeneous sounds. In the experiment, event-related potentials (ERPs) were recorded while participants heard frequently sung consonant-vowel syllables and rare stimuli deviating in either consonant identity only, pitch only, or in both dimensions. Every type of deviation elicited a reliable MMN. As expected, the two single-deviant MMNs had similar amplitudes, but that of the double-deviant MMN was also not significantly different from them. This absence of additivity in the double-deviant MMN suggests that consonant and pitch variations are processed, at least at a pre-attentive level, in an integrated rather than independent way. Domain-specificity of consonants may depend on higher-level processes in the hierarchy of speech perception.

A state-space modeling approach for localization of focal current sources from MEG

State-space modeling is a promising approach for current source reconstruction from magnetoencephalography (MEG) because it constrains the spatiotemporal behavior of inverse solutions in a flexible manner. However, state-space model-based source localization research remains underdeveloped; extraction of spatially focal current sources and handling of the high dimensionality of the distributed source model remain problematic. In this study, we propose a novel state-space model-based method that resolves these problems, extending our previous source localization method to include a temporal constraint by state-space modeling. To enable focal current reconstruction, we account for spatially inhomogeneous temporal dynamics by introducing dynamics model parameters that differ for each cortical position. The model parameters and the intensity of the current sources are jointly estimated according to a bayesian framework. We circumvent the high dimensionality of the problem by assuming prior distributions of the model parameters to reduce the sensitivity to unmodeled components, and by adopting variational bayesian inference to reduce the computational cost. Through simulation experiments and application to real MEG data, we have confirmed that our proposed method successfully reconstructs focal current activities, which evolve with their temporal dynamics.

Improvement of image quality of time-domain diffuse optical tomography with l sparsity regularization

An l(p) (0 < p ≤ 1) sparsity regularization is applied to time-domain diffuse optical tomography with a gradient-based nonlinear optimization scheme to improve the spatial resolution and the robustness to noise. The expression of the l(p) sparsity regularization is reformulated as a differentiable function of a parameter to avoid the difficulty in calculating its gradient in the optimization process. The regularization parameter is selected by the L-curve method. Numerical experiments show that the l(p) sparsity regularization improves the spatial resolution and recovers the difference in the absorption coefficients between two targets, although a target with a small absorption coefficient may disappear due to the strong effect of the l(p) sparsity regularization when the value of p is too small. The l(p) sparsity regularization with small p values strongly localizes the target, and the reconstructed region of the target becomes smaller as the value of p decreases. A phantom experiment validates the numerical simulations.

Differential consequences of orienting attention in parallel and serial search: an ERP study

Previous research has linked attentional effects (such as inhibition of return; IOR) to serial visual search. We investigated different modes of visual search (serial vs. parallel) and demonstrated that the attentional set induced by the type of search greatly influences these attentional effects. IOR was linked to serial search while facilitation followed parallel search. Event related potentials and LORETA source localization data demonstrated that facilitation was associated with a single component, localized in the cuneus and precuneus, while IOR was related to three different components, involving the superior parietal lobe (at around 200 ms), the anterior cingulate cortex and bilateral medial frontal gyrus (~240 ms), and the bilateral superior temporal gyrus, supramarginal gyrus and inferior parietal gyrus (~280 ms). Our results are consistent with the notion that attentional set determines spatial orienting and with previous studies proposing that IOR is not observed in all previously attended locations.

Region-based current-source reconstruction for the inverse EEG problem

This paper presents a new method for the reconstruction of current sources for the electroencephalography (EEG) inverse problem, which produces reconstructed sources, which are confined to a few anatomical regions. The method is based on a partition of the gray matter into a set of regions, and in the construction of a simple linear model for the potential produced by feasible source configurations inside each one of these regions. The proposed method computes the solution in two stages: in the first one, a subset of active regions is found so that the combined potentials produced by sources inside them approximate the measured potential data. In the second stage, a detailed reconstruction of the current sources inside each active region is performed. Experimental results with synthetic data are presented, which show that the proposed scheme is fast, computationally efficient and robust to noise, producing results that are competitive with other published methods, especially when the current sources are effectively distributed in few anatomical regions. The proposed method is also validated with real data from an experiment with visual evoked potentials.

Neuroelectric source imaging using 3SCO: a space coding algorithm based on particle swarm optimization and l0 norm constraint

The electroencephalogram (EEG) neuroelectric sources inverse problem is usually underdetermined and lacks a unique solution, which is due to both the electromagnetism Helmholtz theorem and the fact that there are fewer observations than the unknown variables. One potential choice to tackle this issue is to solve the underdetermined system for a sparse solution. Aiming to the sparse solution, a novel algorithm termed 3SCO (Solution Space Sparse Coding Optimization) is presented in this paper. In 3SCO, after the solution space is coded with some particles, the particle-coded space is compressed by the evolution of particle swarm optimization algorithm, where an l0 constrained fitness function is introduced to guarantee the selection of a suitable sparse solution for the underdetermined system. 3SCO was first tested by localizing simulated EEG sources with different configurations on a realistic head model, and the comparisons with minimum norm (MN), LORETA (low resolution electromagnetic tomography), l1 norm solution and FOCUSS (focal underdetermined system solver) confirmed that a good sparse solution for EEG source imaging could be achieved with 3SCO. Finally, 3SCO was applied to localize the neuroelectric sources in a visual stimuli related experiment and the localized areas were basically consistent with those reported in previous studies.

Equivalent charge source model based iterative maximum neighbor weight for sparse EEG source localization

How to localize the neural electric activities within brain effectively and precisely from the scalp electroencephalogram (EEG) recordings is a critical issue for current study in clinical neurology and cognitive neuroscience. In this paper, based on the charge source model and the iterative re-weighted strategy, proposed is a new maximum neighbor weight based iterative sparse source imaging method, termed as CMOSS (Charge source model based Maximum neighbOr weight Sparse Solution). Different from the weight used in focal underdetermined system solver (FOCUSS) where the weight for each point in the discrete solution space is independently updated in iterations, the new designed weight for each point in each iteration is determined by the source solution of the last iteration at both the point and its neighbors. Using such a new weight, the next iteration may have a bigger chance to rectify the local source location bias existed in the previous iteration solution. The simulation studies with comparison to FOCUSS and LORETA for various source configurations were conducted on a realistic 3-shell head model, and the results confirmed the validation of CMOSS for sparse EEG source localization. Finally, CMOSS was applied to localize sources elicited in a visual stimuli experiment, and the result was consistent with those source areas involved in visual processing reported in previous studies.