A probabilistic algorithm for robust interference suppression in bioelectromagnetic sensor data

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.

Empirical Bayesian localization of event-related time-frequency neural activity dynamics

Accurate reconstruction of the spatio-temporal dynamics of event-related cortical oscillations across human brain regions is an important problem in functional brain imaging and human cognitive neuroscience with magnetoencephalography (MEG) and electroencephalography (EEG). The problem is challenging not only in terms of localization of complex source configurations from sensor measurements with unknown noise and interference but also for reconstruction of transient event-related time-frequency dynamics of cortical oscillations. We recently proposed a robust empirical Bayesian algorithm for simultaneous reconstruction of complex brain source activity and noise covariance, in the context of evoked and resting-state data. In this paper, we expand upon this empirical Bayesian framework for optimal reconstruction of event-related time-frequency dynamics of regional cortical oscillations, referred to as time-frequency Champagne (TFC). This framework enables imaging of five-dimensional (space, time, and frequency) event-related brain activity from M/EEG data, and can be viewed as a time-frequency optimized adaptive Bayesian beamformer. We evaluate TFC in both simulations and several real datasets, with comparisons to benchmark standards - variants of time-frequency optimized adaptive beamformers (TFBF) as well as the sLORETA algorithm. In simulations, we demonstrate several advantages in estimating time-frequency cortical oscillatory dynamics compared to benchmarks. With real MEG data, we demonstrate across many datasets that the proposed approach is robust to highly correlated brain activity and low SNR data, and is able to accurately reconstruct cortical dynamics with data from just a few epochs.

Electromagnetic Source Imaging via Bayesian Modeling with Smoothness in Spatial and Temporal Domains

Accurate reconstruction of cortical activation from electroencephalography and magnetoencephalography (E/MEG) is a long-standing challenge because of the inherently ill-posed inverse problem. In this paper, a novel algorithm under the empirical Bayesian framework, source imaging with smoothness in spatial and temporal domains (SI-SST), is proposed to address this issue. In SI-SST, current sources are decomposed into the product of spatial smoothing kernel, sparseness encoding coefficients, and temporal basis functions (TBFs). Further smoothness is integrated in the temporal domain with the employment of an underlying autoregressive model. Because sparseness encoding coefficients are constructed depending on overlapped clusters over cortex in this model, we derived a novel update rule based on fixed-point criterion instead of the convexity based approach which becomes invalid in this scenario. Entire variables and hyper parameters are updated alternatively in the variational inference procedure. SI-SST was assessed by multiple metrics with both simulated and experimental datasets. In practice, SI-SST had the superior reconstruction performance in both spatial extents and temporal profiles compared to the benchmarks.

Robust estimation of noise for electromagnetic brain imaging with the champagne algorithm

Robust estimation of the number, location, and activity of multiple correlated brain sources has long been a challenging task in electromagnetic brain imaging from M/EEG data, one that is significantly impacted by interference from spontaneous brain activity, sensor noise, and other sources of artifacts. Recently, we introduced the Champagne algorithm, a novel Bayesian inference algorithm that has shown tremendous success in M/EEG source reconstruction. Inherent to Champagne and most other related Bayesian reconstruction algorithms is the assumption that the noise covariance in sensor data can be estimated from “baseline” or “control” measurements. However, in many scenarios, such baseline data is not available, or is unreliable, and it is unclear how best to estimate the noise covariance. In this technical note, we propose several robust methods to estimate the contributions to sensors from noise arising from outside the brain without the need for additional baseline measurements. The incorporation of these methods for diagonal noise covariance estimation improves the robust reconstruction of complex brain source activity under high levels of noise and interference, while maintaining the performance features of Champagne. Specifically, we show that the resulting algorithm, Champagne with noise learning, is quite robust to initialization and is computationally efficient. In simulations, performance of the proposed noise learning algorithm is consistently superior to Champagne without noise learning. We also demonstrate that, even without the use of any baseline data, Champagne with noise learning is able to reconstruct complex brain activity with just a few trials or even a single trial, demonstrating significant improvements in source reconstruction for electromagnetic brain imaging.

NUTMEG: Open Source Software for M/EEG Source Reconstruction

Neurodynamic Utility Toolbox for Magnetoencephalo- and Electroencephalography (NUTMEG) is an open-source MATLAB-based toolbox for the analysis and reconstruction of magnetoencephalography/electroencephalography data in source space. NUTMEG includes a variety of options for the user in data import, preprocessing, source reconstruction, and functional connectivity. A group analysis toolbox allows the user to run a variety of inferential statistics on their data in an easy-to-use GUI-driven format. Importantly, NUTMEG features an interactive five-dimensional data visualization platform. A key feature of NUTMEG is the availability of a large menu of interference cancelation and source reconstruction algorithms. Each NUTMEG operation acts as a stand-alone MATLAB function, allowing the package to be easily adaptable and scripted for the more advanced user for interoperability with other software toolboxes. Therefore, NUTMEG enables a wide range of users access to a complete "sensor-to- source-statistics" analysis pipeline.

Robust Empirical Bayesian Reconstruction of Distributed Sources for Electromagnetic Brain Imaging

Electromagnetic brain imaging is the reconstruction of brain activity from non-invasive recordings of the magnetic fields and electric potentials. An enduring challenge in this imaging modality is estimating the number, location, and time course of sources, especially for the reconstruction of distributed brain sources with complex spatial extent. Here, we introduce a novel robust empirical Bayesian algorithm that enables better reconstruction of distributed brain source activity with two key ideas: kernel smoothing and hyperparameter tiling. Since the proposed algorithm builds upon many of the performance features of the sparse source reconstruction algorithm - Champagne and we refer to this algorithm as Smooth Champagne. Smooth Champagne is robust to the effects of high levels of noise, interference, and highly correlated brain source activity. Simulations demonstrate excellent performance of Smooth Champagne when compared to benchmark algorithms in accurately determining the spatial extent of distributed source activity. Smooth Champagne also accurately reconstructs real MEG and EEG data.

Comparison of DSSP and tSSS algorithms for removing artifacts from vagus nerve stimulators in magnetoencephalography data

OBJECTIVE

Large-amplitude artifacts from vagus nerve stimulator (VNS) implants for refractory epilepsy affect magnetoencephalography (MEG) recordings and are difficult to reject, resulting in unusable data from this important population of patients who are frequently evaluated for surgical treatment of epilepsy. Here we compare the performance of two artifact removal algorithms for MEG data: dual signal subspace projection (DSSP) and temporally extended signal space separation (tSSS).

APPROACH

Each algorithm's performance was first evaluated in simulations. We then tested the performance of each algorithm on resting-state MEG data from patients with VNS implants. We also examined how each algorithm improved source localization of somatosensory evoked fields in patients with VNS implants.

MAIN RESULTS

DSSP and tSSS algorithms have a similar ability to reject interference in both simulated and real MEG data if the origin location for tSSS is appropriately set. If the origin set for tSSS is inappropriate, the signal after tSSS can be distorted due to a mismatch between the internal region and the actual source space. Both DSSP and tSSS are able to remove large-amplitude artifacts from outside the brain. DSSP might be a better choice than tSSS when the choice of origin location for tSSS is difficult.

SIGNIFICANCE

Both DSSP and tSSS algorithms can recover distorted MEG recordings from people with intractable epilepsy and VNS implants, improving epileptic spike identification and source localization of both functional activity and epileptiform activity.

A Novel Scanning Algorithm for MEG/EEG imaging using Covariance Partitioning and Noise Learning

In this paper, we present a novel scanning algorithm, called Covariance Optimization Garnering Noise for Active Cancellation (COGNAC), for magnetoencephalography (MEG) and electroencephalography (EEG) source localization. COGNAC uses a probabilistic graphical generative model for describing sensor data. This novel generative model partitions contributions to sensor data from sources at a particular scan location and from sources outside the scan location, with corresponding multi-resolution variance parameters that are estimated from data. Maximizing a convex upper bound on the marginal likelihood of the data under this generative model results in a cost function that can be optimized efficiently. Importantly, this generative model enables learning of sensor noise without the need for additional baseline or pre-stimulus data. The resulting inference algorithm is quite robust to reconstruction of highly correlated sources and to the effect of high levels of interference and noise sources. Algorithm performance was compared to representative benchmark algorithms on both simulated and real brain activity. In simulations, performance of our novel algorithm is consistently superior to benchmarks. We also demonstrate that the new algorithm is robust to correlated brain activity present in real MEG/EEG data.

Hierarchical multiscale Bayesian algorithm for robust MEG/EEG source reconstruction

In this paper, we present a novel hierarchical multiscale Bayesian algorithm for electromagnetic brain imaging using magnetoencephalography (MEG) and electroencephalography (EEG). In particular, we present a solution to the source reconstruction problem for sources that vary in spatial extent. We define sensor data measurements using a generative probabilistic graphical model that is hierarchical across spatial scales of brain regions and voxels. We then derive a novel Bayesian algorithm for probabilistic inference with this graphical model. This algorithm enables robust reconstruction of sources that have different spatial extent, from spatially contiguous clusters of dipoles to isolated dipolar sources. We compare the new algorithm with several representative benchmarks on both simulated and real brain activities. The source locations and the correct estimation of source time courses used for the simulated data are chosen to test the performance on challenging source configurations. In simulations, performance of the novel algorithm shows superiority to several existing benchmark algorithms. We also demonstrate that the new algorithm is more robust to correlated brain activity present in real MEG and EEG data and is able to resolve distinct and functionally relevant brain areas with real MEG and EEG datasets.

Evaluation of a dual signal subspace projection algorithm in magnetoencephalographic recordings from patients with intractable epilepsy and vagus nerve stimulators

Magnetoencephalography (MEG) data is subject to many sources of environmental noise, and interference rejection is a necessary step in the processing of MEG data. Large amplitude interference caused by sources near the brain have been common in clinical settings and are difficult to reject. Artifact from vagal nerve stimulators (VNS) is a prototypical example. In this study, we describe a novel MEG interference rejection algorithm called dual signal subspace projection (DSSP), and evaluate its performance in clinical MEG data from people with epilepsy and implanted VNS. The performance of DSSP was evaluated in a retrospective cohort study of patients with epilepsy and VNS who had MEG scans for source localization of interictal epileptiform discharges. DSSP was applied to the MEG data and compared with benchmark for performance. We evaluated the clinical impact of interference rejection based on human expert detection and estimation of the location and time-course of interictal spikes, using an empirical Bayesian source reconstruction algorithm (Champagne). Clinical recordings, after DSSP processing, became more readable and a greater number of interictal epileptic spikes could be clearly identified. Source localization results of interictal spikes also significantly improved from those achieved before DSSP processing, including meaningful estimates of activity time courses. Therefore, DSSP is a valuable novel interference rejection algorithm that can be successfully deployed for the removal of strong artifacts and interferences in MEG.

Model-based Bayesian signal extraction algorithm for peripheral nerves

OBJECTIVE

Multi-channel cuff electrodes have recently been investigated for extracting fascicular-level motor commands from mixed neural recordings. Such signals could provide volitional, intuitive control over a robotic prosthesis for amputee patients. Recent work has demonstrated success in extracting these signals in acute and chronic preparations using spatial filtering techniques. These extracted signals, however, had low signal-to-noise ratios and thus limited their utility to binary classification. In this work a new algorithm is proposed which combines previous source localization approaches to create a model based method which operates in real time.

APPROACH

To validate this algorithm, a saline benchtop setup was created to allow the precise placement of artificial sources within a cuff and interference sources outside the cuff. The artificial source was taken from five seconds of chronic neural activity to replicate realistic recordings. The proposed algorithm, hybrid Bayesian signal extraction (HBSE), is then compared to previous algorithms, beamforming and a Bayesian spatial filtering method, on this test data. An example chronic neural recording is also analyzed with all three algorithms.

MAIN RESULTS

The proposed algorithm improved the signal to noise and signal to interference ratio of extracted test signals two to three fold, as well as increased the correlation coefficient between the original and recovered signals by 10-20%. These improvements translated to the chronic recording example and increased the calculated bit rate between the recovered signals and the recorded motor activity.

SIGNIFICANCE

HBSE significantly outperforms previous algorithms in extracting realistic neural signals, even in the presence of external noise sources. These results demonstrate the feasibility of extracting dynamic motor signals from a multi-fascicled intact nerve trunk, which in turn could extract motor command signals from an amputee for the end goal of controlling a prosthetic limb.

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.

Dual signal subspace projection (DSSP): a novel algorithm for removing large interference in biomagnetic measurements

OBJECTIVE

In functional electrophysiological imaging, signals are often contaminated by interference that can be of considerable magnitude compared to the signals of interest. This paper proposes a novel algorithm for removing such interferences that does not require separate noise measurements.

APPROACH

The algorithm is based on a dual definition of the signal subspace in the spatial- and time-domains. Since the algorithm makes use of this duality, it is named the dual signal subspace projection (DSSP). The DSSP algorithm first projects the columns of the measured data matrix onto the inside and outside of the spatial-domain signal subspace, creating a set of two preprocessed data matrices. The intersection of the row spans of these two matrices is estimated as the time-domain interference subspace. The original data matrix is projected onto the subspace that is orthogonal to this interference subspace.

MAIN RESULTS

The DSSP algorithm is validated by using the computer simulation, and using two sets of real biomagnetic data: spinal cord evoked field data measured from a healthy volunteer and magnetoencephalography data from a patient with a vagus nerve stimulator.

SIGNIFICANCE

The proposed DSSP algorithm is effective for removing overlapped interference in a wide variety of biomagnetic measurements.

Automated model selection in covariance estimation and spatial whitening of MEG and EEG signals

Magnetoencephalography and electroencephalography (M/EEG) measure non-invasively the weak electromagnetic fields induced by post-synaptic neural currents. The estimation of the spatial covariance of the signals recorded on M/EEG sensors is a building block of modern data analysis pipelines. Such covariance estimates are used in brain-computer interfaces (BCI) systems, in nearly all source localization methods for spatial whitening as well as for data covariance estimation in beamformers. The rationale for such models is that the signals can be modeled by a zero mean Gaussian distribution. While maximizing the Gaussian likelihood seems natural, it leads to a covariance estimate known as empirical covariance (EC). It turns out that the EC is a poor estimate of the true covariance when the number of samples is small. To address this issue the estimation needs to be regularized. The most common approach downweights off-diagonal coefficients, while more advanced regularization methods are based on shrinkage techniques or generative models with low rank assumptions: probabilistic PCA (PPCA) and factor analysis (FA). Using cross-validation all of these models can be tuned and compared based on Gaussian likelihood computed on unseen data. We investigated these models on simulations, one electroencephalography (EEG) dataset as well as magnetoencephalography (MEG) datasets from the most common MEG systems. First, our results demonstrate that different models can be the best, depending on the number of samples, heterogeneity of sensor types and noise properties. Second, we show that the models tuned by cross-validation are superior to models with hand-selected regularization. Hence, we propose an automated solution to the often overlooked problem of covariance estimation of M/EEG signals. The relevance of the procedure is demonstrated here for spatial whitening and source localization of MEG signals.

Bayesian spatial filters for source signal extraction: a study in the peripheral nerve

The ability to extract physiological source signals to control various prosthetics offer tremendous therapeutic potential to improve the quality of life for patients suffering from motor disabilities. Regardless of the modality, recordings of physiological source signals are contaminated with noise and interference along with crosstalk between the sources. These impediments render the task of isolating potential physiological source signals for control difficult. In this paper, a novel Bayesian Source Filter for signal Extraction (BSFE) algorithm for extracting physiological source signals for control is presented. The BSFE algorithm is based on the source localization method Champagne and constructs spatial filters using Bayesian methods that simultaneously maximize the signal to noise ratio of the recovered source signal of interest while minimizing crosstalk interference between sources. When evaluated over peripheral nerve recordings obtained in vivo, the algorithm achieved the highest signal to noise interference ratio ( 7.00 ±3.45 dB) amongst the group of methodologies compared with average correlation between the extracted source signal and the original source signal R = 0.93. The results support the efficacy of the BSFE algorithm for extracting source signals from the peripheral nerve.

Resting state α-band functional connectivity and recovery after stroke

After cerebral ischemia, disruption and subsequent reorganization of functional connections occur both locally and remote to the lesion. However, the unpredictable timing and extent of sensorimotor recovery reflects a gap in understanding of these underlying neural mechanisms. We aimed to identify the plasticity of alpha-band functional neural connections within the perilesional area and the predictive value of functional connectivity with respect to motor recovery of the upper extremity after stroke. Our results show improvements in upper extremity motor recovery in relation to distributed changes in MEG-based alpha band functional connectivity, both in the perilesional area and contralesional cortex. Motor recovery was found to be predicted by increased connectivity at baseline in the ipsilesional somatosensory area, supplementary motor area, and cerebellum, contrasted with reduced connectivity of contralesional motor regions, after controlling for age, stroke onset-time and lesion size. These findings support plasticity within a widely distributed neural network and define brain regions in which the extent of network participation predicts post-stroke recovery potential.

Extraction of control signals from a mixture of source activity in the peripheral nerve

Extracting physiological signals to control external devices such as prosthetics is a field of research that offers great hope for patients suffering from disabilities. In this paper, we present an algorithm for isolating control signals from peripheral nerve cuff recordings. The algorithm is able to extract individual control signals from a mixture of source signal activity while maximizing SNR and minimizing cross-talk between the control signals. Based on fast independent component analysis FICA and an adaptation of Champagne, the proposed algorithm is tested against previously published results obtained using beamforming techniques in an acute preparation of rabbits. Preliminary results demonstrate an improvement in performance.

Performance evaluation of the Champagne source reconstruction algorithm on simulated and real M/EEG data

In this paper, we present an extensive performance evaluation of a novel source localization algorithm, Champagne. It is derived in an empirical Bayesian framework that yields sparse solutions to the inverse problem. It is robust to correlated sources and learns the statistics of non-stimulus-evoked activity to suppress the effect of noise and interfering brain activity. We tested Champagne on both simulated and real M/EEG data. The source locations used for the simulated data were chosen to test the performance on challenging source configurations. In simulations, we found that Champagne outperforms the benchmark algorithms in terms of both the accuracy of the source localizations and the correct estimation of source time courses. We also demonstrate that Champagne is more robust to correlated brain activity present in real MEG data and is able to resolve many distinct and functionally relevant brain areas with real MEG and EEG data.

MEG beamforming using Bayesian PCA for adaptive data covariance matrix regularization

Beamformers are a commonly used method for doing source localization from magnetoencephalography (MEG) data. A key ingredient in a beamformer is the estimation of the data covariance matrix. When the noise levels are high, or when there is only a small amount of data available, the data covariance matrix is estimated poorly and the signal-to-noise ratio (SNR) of the beamformer output degrades. One solution to this is to use regularization whereby the diagonal of the covariance matrix is amplified by a pre-specified amount. However, this provides improvements at the expense of a loss in spatial resolution, and the parameter controlling the amount of regularization must be chosen subjectively. In this paper, we introduce a method that provides an adaptive solution to this problem by using a Bayesian Principle Component Analysis (PCA). This provides an estimate of the data covariance matrix to give a data-driven, non-arbitrary solution to the trade-off between the spatial resolution and the SNR of the beamformer output. This also provides a method for determining when the quality of the data covariance estimate maybe under question. We apply the approach to simulated and real MEG data, and demonstrate the way in which it can automatically adapt the regularization to give good performance over a range of noise and signal levels.

MEG/EEG source reconstruction, statistical evaluation, and visualization with NUTMEG

NUTMEG is a source analysis toolbox geared towards cognitive neuroscience researchers using MEG and EEG, including intracranial recordings. Evoked and unaveraged data can be imported to the toolbox for source analysis in either the time or time-frequency domains. NUTMEG offers several variants of adaptive beamformers, probabilistic reconstruction algorithms, as well as minimum-norm techniques to generate functional maps of spatiotemporal neural source activity. Lead fields can be calculated from single and overlapping sphere head models or imported from other software. Group averages and statistics can be calculated as well. In addition to data analysis tools, NUTMEG provides a unique and intuitive graphical interface for visualization of results. Source analyses can be superimposed onto a structural MRI or headshape to provide a convenient visual correspondence to anatomy. These results can also be navigated interactively, with the spatial maps and source time series or spectrogram linked accordingly. Animations can be generated to view the evolution of neural activity over time. NUTMEG can also display brain renderings and perform spatial normalization of functional maps using SPM's engine. As a MATLAB package, the end user may easily link with other toolboxes or add customized functions.

An algorithm for source signal extraction from the peripheral nerve

Extracting physiological signals to control external devices such as prosthetics is a field of research that offers great hope for patients suffering from disabilities. In this paper, a novel source signal extraction algorithm, based on the source localization method Champagne, is presented. The algorithm constructs spatial filters that not only maximizes the signal to noise ratio (SNR > 13 dB) of the source activities but also minimizes the cross-talk interference between the sources 10log((P(source of interest)/P(interference sources)) > 14 dB.

Accurate reconstruction of brain activity and functional connectivity from noisy MEG data

The synchronous brain activity measured via magnetoencephalography (MEG) arises from current dipoles located throughout the cortex. Estimating the number, location, time-course, and orientation of these dipoles, called sources, remains a challenging task, one that is significantly compounded by the effects of source correlations and interference from spontaneous brain activity and sensor noise. Likewise, assessing the interactions between the individual sources, known as functional connectivity, is also confounded by noise and correlations in the sensor recordings. Computational complexity has been an obstacle to computing functional connectivity. This paper demonstrates the application of an empirical Bayesian method to perform source localization with MEG data in order to estimate measures of functional connectivity. We demonstrate that brain source activity inferred from this algorithm is better suited to uncover the interactions between brain areas as compared to other commonly used source localization algorithms.

Source localization of EEG/MEG data by correlating columns of ICA and lead field matrices

Independent components analysis (ICA) has previously been used to denoise EEG/magnetoencephalography (MEG) signals before performing neural source localization. Source localization is then performed using a method such as beamforming or dipole fitting. Here we show how ICA can also be used as a source localization method, negating the need for beamforming and dipole fitting. This type of approach is valid whenever an estimate of the forward (mixing) model for all putative source locations is available, which includes EEG and MEG applications. The proposed method consists of estimating the forward model using the laws of physics, estimating a second forward model using ICA, and then correlating the columns of the matrices that represent the two forward models. We show that, when synthetic data are used, the proposed localization method produces a smaller localization error than several alternatives. We also show localization results for real auditory-evoked MEG data.

Robust Bayesian estimation of the location, orientation, and time course of multiple correlated neural sources using MEG

The synchronous brain activity measured via MEG (or EEG) can be interpreted as arising from a collection (possibly large) of current dipoles or sources located throughout the cortex. Estimating the number, location, and time course of these sources remains a challenging task, one that is significantly compounded by the effects of source correlations and unknown orientations and by the presence of interference from spontaneous brain activity, sensor noise, and other artifacts. This paper derives an empirical Bayesian method for addressing each of these issues in a principled fashion. The resulting algorithm guarantees descent of a cost function uniquely designed to handle unknown orientations and arbitrary correlations. Robust interference suppression is also easily incorporated. In a restricted setting, the proposed method is shown to produce theoretically zero reconstruction error estimating multiple dipoles even in the presence of strong correlations and unknown orientations, unlike a variety of existing Bayesian localization methods or common signal processing techniques such as beamforming and sLORETA. Empirical results on both simulated and real data sets verify the efficacy of this approach.

Probabilistic algorithms for MEG/EEG source reconstruction using temporal basis functions learned from data

We present two related probabilistic methods for neural source reconstruction from MEG/EEG data that reduce effects of interference, noise, and correlated sources. Both methods localize source activity using a linear mixture of temporal basis functions (TBFs) learned from the data. In contrast to existing methods that use predetermined TBFs, we compute TBFs from data using a graphical factor analysis based model [Nagarajan, S.S., Attias, H.T., Hild, K.E., Sekihara, K., 2007a. A probabilistic algorithm for robust interference suppression in bioelectromagnetic sensor data. Stat Med 26, 3886-3910], which separates evoked or event-related source activity from ongoing spontaneous background brain activity. Both algorithms compute an optimal weighting of these TBFs at each voxel to provide a spatiotemporal map of activity across the brain and a source image map from the likelihood of a dipole source at each voxel. We explicitly model, with two different robust parameterizations, the contribution from signals outside a voxel of interest. The two models differ in a trade-off of computational speed versus accuracy of learning the unknown interference contributions. Performance in simulations and real data, both with large noise and interference and/or correlated sources, demonstrates significant improvement over existing source localization methods.