Multiple Sparse Priors Research Articles

Assessing dynamic brain activity during verbal associative learning using MEG/fMRI co-processing

BackgroundThe abilities of individual neuroimaging methods to resolve spatial and temporal contributions of brain regions during cognitive processes are limited. Co-processing of functional magnetic resonance imaging (fMRI) and magnetoencephalography (MEG) may overcome some of the limitations by utilizing Multiple Sparse Priors (MSP) in a Bayesian framework that takes advantage of the temporal resolution of MEG and spatial resolution of fMRI. Methods24 healthy participants were recruited to perform a paired-associate verbal learning task during fMRI and MEG scans. FMRI data were processed within Group ICA fMRI Toolbox. Independent components (ICs) were temporally sorted by task time series (|r|>0.30 threshold identified task-related ICs). Task-positive (“generate”) ICs were retained as spatial priors for MEG analyses. MEG data were processed by an event-related potential (ERP) approach and with a theta power approach. MEG source reconstructions were constrained within the task-positive ICs for both ERP and theta-power approaches. ResultsFor fMRI, five networks were identified as task-related. Four ICs underlying active generation spanned bilateral parietal, orbitofrontal, medial frontal and superior temporal regions, and occipital lobe. FMRI-constrained MEG source reconstructions using the ERP approach yielded early visual cortex activity followed by left inferior frontal gyrus (IFG) and orbito-frontal cortex (OFC) recruitment to coalesce in the left inferior temporal lobe. For the theta approach, MEG source reconstructions showed a progression of activity from bilateral temporal areas to left OFC and middle temporal gyrus, followed by right IFG. DiscussionMSP analyses informed by fMRI produced more focused regional activity than reconstructions without priors suggesting this approach may result in identifying more relevant semantic information during active generation. Constraining MEG source reconstruction to fMRI priors during active generation indicates fronto-temporal and fronto-parietal networks are interconnected across time and space.

Dual-Branch Discrimination Network Using Multiple Sparse Priors for Image Deblurring.

Blind image deblurring is a challenging problem in computer vision, aiming to restore the sharp image from blurred observation. Due to the incompatibility between the complex unknown degradation and the simple synthetic model, directly training a deep convolutional neural network (CNN) usually cannot sufficiently handle real-world blurry images. An existed generative adversarial network (GAN) can generate more detailed and realistic images, but the game between generator and discriminator is unbalancing, which leads to the training parameters not being able to converge to the ideal Nash equilibrium points. In this paper, we propose a GAN with a dual-branch discriminator using multiple sparse priors for image deblurring (DBSGAN) to overcome this limitation. By adding the multiple sparse priors into the other branch of the discriminator, the task of the discriminator is more complex. It can balance the game between the generator and the discriminator. Extensive experimental results on both synthetic and real-world blurry image datasets demonstrate the superior performance of our method over the state of the art in terms of quantitative metrics and visual quality. Especially for the GOPRO dataset, the averaged PSNR improves over others.

Optimizing EEG Source Reconstruction with Concurrent fMRI-Derived Spatial Priors

Reconstructing EEG sources involves a complex pipeline, with the inverse problem being the most challenging. Multiple inversion algorithms are being continuously developed, aiming to tackle the non-uniqueness of this problem, which has been shown to be partially circumvented by including prior information in the inverse models. Despite a few efforts, there are still current and persistent controversies regarding the inversion algorithm of choice and the optimal set of spatial priors to be included in the inversion models. The use of simultaneous EEG-fMRI data is one approach to tackle this problem. The spatial resolution of fMRI makes fMRI derived spatial priors very convenient for EEG reconstruction, however, only task activation maps and resting-state networks (RSNs) have been explored so far, overlooking the recent, but already accepted, notion that brain networks exhibit dynamic functional connectivity fluctuations. The lack of a systematic comparison between different source reconstruction algorithms, considering potentially more brain-informative priors such as fMRI, motivates the search for better reconstruction models. Using simultaneous EEG-fMRI data, here we compared four different inversion algorithms (minimum norm, MN; low resolution electromagnetic tomography, LORETA; empirical Bayes beamformer, EBB; and multiple sparse priors, MSP) under a Bayesian framework (as implemented in SPM), each with three different sets of priors consisting of: (1) those specific to the algorithm; (2) those specific to the algorithm plus fMRI task activation maps and RSNs; and (3) those specific to the algorithm plus fMRI task activation maps and RSNs and network modules of task-related dFC states estimated from the dFC fluctuations. The quality of the reconstructed EEG sources was quantified in terms of model-based metrics, namely the expectation of the posterior probability P(model|data) and variance explained of the inversion models, and the overlap/proportion of brain regions known to be involved in the visual perception tasks that the participants were submitted to, and RSN templates, with/within EEG source components. Model-based metrics suggested that model parsimony is preferred, with the combination MSP and priors specific to this algorithm exhibiting the best performance. However, optimal overlap/proportion values were found using EBB and priors specific to this algorithm and fMRI task activation maps and RSNs or MSP and considering all the priors (algorithm priors, fMRI task activation maps and RSNs and dFC state modules), respectively, indicating that fMRI spatial priors, including dFC state modules, might contain useful information to recover EEG source components reflecting neuronal activity of interest. Our main results show that providing fMRI spatial derived priors that reflect the dynamics of the brain might be useful to map neuronal activity more accurately from EEG-fMRI. Furthermore, this work paves the way towards a more informative selection of the optimal EEG source reconstruction approach, which may be critical in future studies.

Dynamic causal modeling of evoked responses during emergency braking: an ERP study.

Describing a neural activity map based on observed responses in emergency situations, especially during driving, is a challenging issue that would help design driver-assistant devices and a better understanding of the brain. This study aimed to investigate which regions were involved during emergency braking, measuring the interactions and strength of the connections and describing coupling among these brain regions by dynamic causal modeling (DCM) parameters that we extracted from event-related potential signals, which were then estimated based on emergency braking data with visual stimulation. The data were reanalyzed from a simulator study, which was designed to create emergency situations for participants during a simple driving task. The experimental protocol includes driving a virtual reality car, and the subjects were exposed to emergency situations in a simulator system, while electroencephalogram, electro-oculogram, and electromyogram signals were recorded. In this research, locations of active brain regions in montreal neurological institute coordinates from event-related responses were identified using multiple sparse priors method, in which sensor space was allocated to resource space. Source localization results revealed nine active regions. After applying DCM on data, a proposed model during emergency braking for all people was obtained. The braking response time was defined based on the first noticeable (above noise-level) braking pedal deflection after an induced braking maneuver. The result revealed a significant difference in response time between subjects who have the lateral connection between visual cortex, visual processing, and detecting objects areas have shorter response time (p-value = 0.05) than the subjects who do not have such connections.

Source localization of epileptic spikes using Multiple Sparse Priors

ObjectiveTo evaluate epileptic source estimation using multiple sparse priors (MSP) inverse method and high-resolution, individual electrical head models. MethodsAccurate source localization is dependent on accurate electrical head models and appropriate inverse solvers. Using high-resolution, individual electrical head models in fifteen epilepsy patients, with surgical resection and clinical outcome as criteria for accuracy, performance of MSP method was compared against standardized low-resolution brain electromagnetic tomography (sLORETA) and coherent maximum entropy on the mean (cMEM) methods. ResultsThe MSP method performed similarly to the sLORETA method and slightly better than the cMEM method in terms of success rate. The MSP and cMEM methods were more focal than sLORETA with the advantage of not requiring an arbitrary selection of a hyperparameter or thresholding of reconstructed current density values to determine focus. MSP and cMEM methods were better than sLORETA in terms of spatial dispersion. ConclusionsResults suggest that the three methods are complementary and could be used together. In practice, the MSP method will be easier to use and interpret compared to sLORETA, and slightly more accurate and faster than the cMEM method. SignificanceSource localization of interictal spikes from dense-array electroencephalography data has been shown to be a reliable marker of epileptic foci and useful for pre-surgical planning. The advantages of MSP make it a useful complement to other inverse solvers in clinical practice.

Low-Density EEG for Neural Activity Reconstruction Using Multivariate Empirical Mode Decomposition.

Several approaches can be used to estimate neural activity. The main differences between them concern the a priori information used and its sensitivity to high noise levels. Empirical mode decomposition (EMD) has been recently applied to electroencephalography EEG-based neural activity reconstruction to provide a priori time-frequency information to improve the estimation of neural activity. EMD has the specific ability to identify independent oscillatory modes in non-stationary signals with multiple oscillatory components. However, attempts to use EMD in EEG analysis have not yet provided optimal reconstructions, due to the intrinsic mode-mixing problem of EMD. Several studies have used single-channel analysis, whereas others have used multiple-channel analysis for other applications. Here, we present the results of multiple-channel analysis using multivariate empirical mode decomposition (MEMD) to reduce the mode-mixing problem and provide useful a priori time-frequency information for the reconstruction of neuronal activity using several low-density EEG electrode montages. The methods were evaluated using real and synthetic EEG data, in which the reconstructions were performed using the multiple sparse priors (MSP) algorithm with EEG electrode montages of 32, 16, and 8 electrodes. The quality of the source reconstruction was assessed using the Wasserstein metric. A comparison of the solutions without pre-processing and those after applying MEMD showed the source reconstructions to be improved using MEMD as a priori information for the low-density montages of 8 and 16 electrodes. The mean source reconstruction error on a real EEG dataset was reduced by 59.42 and 66.04% for the 8 and 16 electrode montages, respectively, and that on a simulated EEG with three active sources, by 87.31 and 31.45% for the same electrode montages.

Comparison of Machine Learning Techniques Based Brain Source Localization Using EEG Signals

The brain is the most complex organ of the human body with millions of connections and activations. The electromagnetic signals are generated inside the brain due to a mental or physical task performed. These signals excite a bunch of neurons within a particular lobe depending upon the nature of the task performed. To localize this activity, certain machine learning (ML) techniques in conjunction with a neuroimaging technique (M/EEG, fMRI, PET) are developed. Different ML techniques are provided in the literature for brain source localization. Among them, the most common are: minimum norm estimation (MNE), low resolution brain electromagnetic tomography (LORETA) and Bayesian framework based multiple sparse priors (MSP). In this research work, EEG is used as a neuroimaging technique. EEG data is synthetically generated at SNR=5dB. Afterwards, ML techniques are applied to estimate the active sources. Each dataset is run for multiple trials (>40). The performance is analyzed using free energy and localization error as performance indicators. Furthermore, MSP is applied with a variant number of patches to observe the impact of patches on source localization. It is observed that with an increased number of patches, the sources are localized with more precision and accuracy as expressed in terms of free energy and localization error, respectively. The patches optimization within the Bayesian Framework produces improved results in terms of free energy and localization error.

Multiple sparse priors technique with optimized patches for brain source localization

AbstractLocalizing brain neural activity using electroencephalography (EEG) neuroimaging technique is getting increasing response from neuroscience researchers and medical community. It is due to the fact that brain source localization has a variety of applications for diagnoses of various brain disorders. This problem is ill‐posed in nature because an infinite number of source configurations can produce the same potential at the head surface. Recently, a new technique that is based on Bayesian framework, called the multiple sparse priors (MSP), was proposed as a solution to this problem. The MSP develops the solution for source localization using the current densities associated with dipoles in terms of prior source covariance matrix and sensor covariance matrix, respectively. Then, it uses the maximization of the cost function of the free energy under the assumption of a fixed number of hyperparameters or patches in order to obtain the elements of prior source covariance matrix. This research work aims to further enhance the maximization process of MSP with regard to the free energy by considering a variable number of patches. This will lead to a better estimation of brain sources in terms of localization errors. The performance of the modified MSP with a variable number of patches is compared with the original MSP using simulated and real‐time EEG data. The results show a significant improvement in terms of localization errors.

Effective connectivity of mental fatigue: Dynamic causal modeling of EEG data.

Recognition of sources in the brain and their interaction with mental fatigue states are interesting subjects for researchers. The aim of this study was to investigate the mental fatigue effects on brain areas by dynamic casual modeling (DCM) parameters that are extracted from event-related potential (ERP) signals which were then estimated based on mental fatigue data with visual stimulation. ERP were recorded based on a Continuous Performance Task in four consecutive trials. Active regions and brain sources were extracted by a Multiple Sparse Priors algorithm. Four models are proposed for DCM. The parameters and the structure of the best model were obtained by SPM software for ERP in each of the four trials. The results illustrate that an increase of mental fatigue through trials leads to increased likelihood of choosing forward models.

Compressed Sensing MRI Reconstruction with Multiple Sparsity Constraints on Radial Sampling

Compressed Sensing Magnetic Resonance Imaging (CS-MRI) is a promising technique for accelerating MRI acquisitions by using fewer k-space data. Exploiting more sparsity is an important approach to improving the CS-MRI reconstruction quality. We propose a novel CS-MRI framework based on multiple sparse priors to increase reconstruction accuracy. The wavelet sparsity, wavelet tree structured sparsity, and nonlocal total variation (NLTV) regularizations were integrated in the CS-MRI framework, and the optimization problem was solved using a fast composite splitting algorithm (FCSA). The proposed method was evaluated on different types of MR images with different radial sampling schemes and different sampling ratios and compared with the state-of-the-art CS-MRI reconstruction methods in terms of peak signal-to-noise ratio (PSNR), feature similarity (FSIM), relative l2 norm error (RLNE), and mean structural similarity (MSSIM). The results demonstrated that the proposed method outperforms the traditional CS-MRI algorithms in both visual and quantitative comparisons.

Localization of Active Brain Sources From EEG Signals Using Empirical Mode Decomposition: A Comparative Study.

The localization of active brain sources from Electroencephalogram (EEG) is a useful method in clinical applications, such as the study of localized epilepsy, evoked-related-potentials, and attention deficit/hyperactivity disorder. The distributed-source model is a common method to estimate neural activity in the brain. The location and amplitude of each active source are estimated by solving the inverse problem by regularization or using Bayesian methods with spatio-temporal constraints. Frequency and spatio-temporal constraints improve the quality of the reconstructed neural activity. However, separation into frequency bands is beneficial when the relevant information is in specific sub-bands. We improved frequency-band identification and preserved good temporal resolution using EEG pre-processing techniques with good frequency band separation and temporal resolution properties. The identified frequency bands were included as constraints in the solution of the inverse problem by decomposing the EEG signals into frequency bands through various methods that offer good frequency and temporal resolution, such as empirical mode decomposition (EMD) and wavelet transform (WT). We present a comparative analysis of the accuracy of brain-source reconstruction using these techniques. The accuracy of the spatial reconstruction was assessed using the Wasserstein metric for real and simulated signals. We approached the mode-mixing problem, inherent to EMD, by exploring three variants of EMD: masking EMD, Ensemble-EMD (EEMD), and multivariate EMD (MEMD). The results of the spatio-temporal brain source reconstruction using these techniques show that masking EMD and MEMD can largely mitigate the mode-mixing problem and achieve a good spatio-temporal reconstruction of the active sources. Masking EMD and EEMD achieved better reconstruction than standard EMD, Multiple Sparse Priors, or wavelet packet decomposition when EMD was used as a pre-processing tool for the spatial reconstruction (averaged over time) of the brain sources. The spatial resolution obtained using all three EMD variants was substantially better than the use of EMD alone, as the mode-mixing problem was mitigated, particularly with masking EMD and EEMD. These findings encourage further exploration into the use of EMD-based pre-processing, the mode-mixing problem, and its impact on the accuracy of brain source activity reconstruction.

Quantifying the performance of MEG source reconstruction using resting state data

In magnetoencephalography (MEG) research there are a variety of inversion methods to transform sensor data into estimates of brain activity. Each new inversion scheme is generally justified against a specific simulated or task scenario. The choice of this scenario will however have a large impact on how well the scheme performs. We describe a method with minimal selection bias to quantify algorithm performance using human resting state data. These recordings provide a generic, heterogeneous, and plentiful functional substrate against which to test different MEG recording and reconstruction approaches. We used a Hidden Markov model to spatio-temporally partition data into self-similar dynamic states. To test the anatomical precision that could be achieved, we then inverted these data onto libraries of systematically distorted subject-specific cortical meshes and compared the quality of the fit using cross validation and a Free energy metric. This revealed which inversion scheme was able to identify the least distorted (most accurate) anatomical models, and allowed us to quantify an upper bound on the mean anatomical distortion accordingly. We used two resting state datasets, one recorded with head-casts and one without. In the head-cast data, the Empirical Bayesian Beamformer (EBB) algorithm showed the best mean anatomical discrimination (3.7 mm) compared with Minimum Norm/LORETA (6.0 mm) and Multiple Sparse Priors (9.4 mm). This pattern was replicated in the second (conventional dataset) although with a marginally poorer (non-significant) prediction of the missing (cross-validated) data. Our findings suggest that the abundant resting state data now commonly available could be used to refine and validate MEG source reconstruction methods and/or recording paradigms.

Brain source localization using reduced EEG sensors

Brain source activation is caused due to certain mental or physical task, and such activation is localized by using various optimization techniques. This localization has vital application for diagnoses of various brain disorders such as epilepsy, schizophrenia, Alzheimer, depression, Parkinson and stress. Various neuroimaging techniques (such as EEG, fMRI, MEG) are used to record brain activity for inference and estimation of active source locations. EEG employs set of sensors which are placed on scalp to measure electric potentials. These sensors have significant role in overall system complexity, computational time and system cost. Hence, sensor reduction for EEG source localization has been a topic of interest for researchers to develop a system with improved localization precision, less system complexity and reduced cost. This research work discusses and implements the brain source localization for real-time and synthetically generated EEG dataset with reduced number of sensors. For this, various optimization algorithms are used which include Bayesian framework-based multiple sparse priors (MSP), classical low-resolution brain electromagnetic tomography (LORETA), beamformer and minimum norm estimation (MNE). The results obtained are then compared in terms of negative variational free energy, localization error and computational time measured in seconds. It is observed that multiple sparse priors (MSP) with increased number of patches performed best even with reduced number of sensors, i.e., 7 instead of 74. The results are shown valid for synthetic EEG data at low SNR level, i.e., 5 dB and real-time EEG data, respectively.

Non-invasive laminar inference with MEG: Comparison of methods and source inversion algorithms

Magnetoencephalography (MEG) is a direct measure of neuronal current flow; its anatomical resolution is therefore not constrained by physiology but rather by data quality and the models used to explain these data. Recent simulation work has shown that it is possible to distinguish between signals arising in the deep and superficial cortical laminae given accurate knowledge of these surfaces with respect to the MEG sensors. This previous work has focused around a single inversion scheme (multiple sparse priors) and a single global parametric fit metric (free energy). In this paper we use several different source inversion algorithms and both local and global, as well as parametric and non-parametric fit metrics in order to demonstrate the robustness of the discrimination between layers. We find that only algorithms with some sparsity constraint can successfully be used to make laminar discrimination. Importantly, local t-statistics, global cross-validation and free energy all provide robust and mutually corroborating metrics of fit. We show that discrimination accuracy is affected by patch size estimates, cortical surface features, and lead field strength, which suggests several possible future improvements to this technique. This study demonstrates the possibility of determining the laminar origin of MEG sensor activity, and thus directly testing theories of human cognition that involve laminar- and frequency-specific mechanisms. This possibility can now be achieved using recent developments in high precision MEG, most notably the use of subject-specific head-casts, which allow for significant increases in data quality and therefore anatomically precise MEG recordings. SectionAnalysis methods. ClassificationsSource localization: inverse problem; Source localization: other.

Regional brain activity that determines successful and unsuccessful working memory formation.

Using EEG source reconstruction with Multiple Sparse Priors (MSP), we investigated the regional brain activity that determines successful memory encoding in two participant groups of high and low accuracy rates. Eighteen healthy young adults performed a sequential fashion of visual Sternberg memory task. The 32-channel EEG was continuously measured during participants performed two 70 trials of memory task. The regional brain activity corresponding to the oscillatory EEG activity in the alpha band (8-13 Hz) during encoding period was analyzed by MSP implemented in SPM8. We divided the data of all participants into 2 groups (low- and highperformance group) and analyzed differences in regional brain activity between trials in which participants answered correctly and incorrectly within each of the group. Participants in low-performance group showed significant activity increase in the visual cortices in their successful trials compared to unsuccessful ones. On the other hand, those in high-performance group showed a significant activity increase in widely distributed cortical regions in the frontal, temporal, and parietal areas including those suggested as Baddeley's working memory model. Further comparison of activated cortical volumes and mean current source intensities within the cortical regions of Baddeley's model during memory encoding demonstrated that participants in high-performance group showed enhanced activity in the right premotor cortex, which plays an important role in maintaining visuospatial attention, compared to those in low performance group. Our results suggest that better ability in memory encoding is associated with distributed and stronger regional brain activities including the premotor cortex, possibly indicating efficient allocation of cognitive load and maintenance of attention.

Integrated Analysis of EEG and fMRI Using Sparsity of Spatial Maps.

Integration of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) is an open problem, which has motivated many researches. The most important challenge in EEG-fMRI integration is the unknown relationship between these two modalities. In this paper, we extract the same features (spatial map of neural activity) from both modality. Therefore, the proposed integration method does not need any assumption about the relationship of EEG and fMRI. We present a source localization method from scalp EEG signal using jointly fMRI analysis results as prior spatial information and source separation for providing temporal courses of sources of interest. The performance of the proposed method is evaluated quantitatively along with multiple sparse priors method and sparse Bayesian learning with the fMRI results as prior information. Localization bias and source distribution index are used to measure the performance of different localization approaches with or without a variety of fMRI-EEG mismatches on simulated realistic data. The method is also applied to experimental data of face perception of 16 subjects. Simulation results show that the proposed method is significantly stable against the noise with low localization bias. Although the existence of an extra region in the fMRI data enlarges localization bias, the proposed method outperforms the other methods. Conversely, a missed region in the fMRI data does not affect the localization bias of the common sources in the EEG-fMRI data. Results on experimental data are congruent with previous studies and produce clusters in the fusiform and occipital face areas (FFA and OFA, respectively). Moreover, it shows high stability in source localization against variations in different subjects.

Electrical source imaging of interictal spikes using multiple sparse volumetric priors for presurgical epileptogenic focus localization.

Electrical source imaging of interictal spikes observed in EEG recordings of patients with refractory epilepsy provides useful information to localize the epileptogenic focus during the presurgical evaluation. However, the selection of the time points or time epochs of the spikes in order to estimate the origin of the activity remains a challenge. In this study, we consider a Bayesian EEG source imaging technique for distributed sources, i.e. the multiple volumetric sparse priors (MSVP) approach. The approach allows to estimate the time courses of the intensity of the sources corresponding with a specific time epoch of the spike. Based on presurgical averaged interictal spikes in six patients who were successfully treated with surgery, we estimated the time courses of the source intensities for three different time epochs: (i) an epoch starting 50 ms before the spike peak and ending at 50% of the spike peak during the rising phase of the spike, (ii) an epoch starting 50 ms before the spike peak and ending at the spike peak and (iii) an epoch containing the full spike time period starting 50 ms before the spike peak and ending 230 ms after the spike peak. To identify the primary source of the spike activity, the source with the maximum energy from 50 ms before the spike peak till 50% of the spike peak was subsequently selected for each of the time windows. For comparison, the activity at the spike peaks and at 50% of the peaks was localized using the LORETA inversion technique and an ECD approach. Both patient-specific spherical forward models and patient-specific 5-layered finite difference models were considered to evaluate the influence of the forward model. Based on the resected zones in each of the patients, extracted from post-operative MR images, we compared the distances to the resection border of the estimated activity. Using the spherical models, the distances to the resection border for the MSVP approach and each of the different time epochs were in the same range as the LORETA and ECD techniques. We found distances smaller than 23 mm, with robust results for all the patients. For the finite difference models, we found that the distances to the resection border for the MSVP inversions of the full spike time epochs were generally smaller compared to the MSVP inversions of the time epochs before the spike peak. The results also suggest that the inversions using the finite difference models resulted in slightly smaller distances to the resection border compared to the spherical models. The results we obtained are promising because the MSVP approach allows to study the network of the estimated source-intensities and allows to characterize the spatial extent of the underlying sources.

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 l1norm 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.

Multiple sparse volumetric priors for distributed EEG source reconstruction

We revisit the multiple sparse priors (MSP) algorithm implemented in the statistical parametric mapping software (SPM) for distributed EEG source reconstruction (Friston et al., 2008). In the present implementation, multiple cortical patches are introduced as source priors based on a dipole source space restricted to a cortical surface mesh. In this note, we present a technique to construct volumetric cortical regions to introduce as source priors by restricting the dipole source space to a segmented gray matter layer and using a region growing approach. This extension allows to reconstruct brain structures besides the cortical surface and facilitates the use of more realistic volumetric head models including more layers, such as cerebrospinal fluid (CSF), compared to the standard 3-layered scalp-skull-brain head models. We illustrated the technique with ERP data and anatomical MR images in 12 subjects. Based on the segmented gray matter for each of the subjects, cortical regions were created and introduced as source priors for MSP-inversion assuming two types of head models. The standard 3-layered scalp–skull–brain head models and extended 4-layered head models including CSF. We compared these models with the current implementation by assessing the free energy corresponding with each of the reconstructions using Bayesian model selection for group studies. Strong evidence was found in favor of the volumetric MSP approach compared to the MSP approach based on cortical patches for both types of head models. Overall, the strongest evidence was found in favor of the volumetric MSP reconstructions based on the extended head models including CSF. These results were verified by comparing the reconstructed activity. The use of volumetric cortical regions as source priors is a useful complement to the present implementation as it allows to introduce more complex head models and volumetric source priors in future studies.

Localization of MEG human brain responses to retinotopic visual stimuli with contrasting source reconstruction approaches.

Magnetoencephalography (MEG) allows the physiological recording of human brain activity at high temporal resolution. However, spatial localization of the source of the MEG signal is an ill-posed problem as the signal alone cannot constrain a unique solution and additional prior assumptions must be enforced. An adequate source reconstruction method for investigating the human visual system should place the sources of early visual activity in known locations in the occipital cortex. We localized sources of retinotopic MEG signals from the human brain with contrasting reconstruction approaches (minimum norm, multiple sparse priors, and beamformer) and compared these to the visual retinotopic map obtained with fMRI in the same individuals. When reconstructing brain responses to visual stimuli that differed by angular position, we found reliable localization to the appropriate retinotopic visual field quadrant by a minimum norm approach and by beamforming. Retinotopic map eccentricity in accordance with the fMRI map could not consistently be localized using an annular stimulus with any reconstruction method, but confining eccentricity stimuli to one visual field quadrant resulted in significant improvement with the minimum norm. These results inform the application of source analysis approaches for future MEG studies of the visual system, and indicate some current limits on localization accuracy of MEG signals.