Electromagnetic Brain Source Imaging by Means of a Robust Minimum Variance Beamformer

Structured noise champagne: an empirical Bayesian algorithm for electromagnetic brain imaging with structured noise

Introduction

Electromagnetic brain imaging is the reconstruction of brain activity from non-invasive recordings of electroencephalography (EEG), magnetoencephalography (MEG), and also from invasive ones such as the intracranial recording of electrocorticography (ECoG), intracranial electroencephalography (iEEG), and stereo electroencephalography EEG (sEEG). These modalities are widely used techniques to study the function of the human brain. Efficient reconstruction of electrophysiological activity of neurons in the brain from EEG/MEG measurements is important for neuroscience research and clinical applications. An enduring challenge in this field is the accurate inference of brain signals of interest while accounting for all sources of noise that contribute to the sensor measurements. The statistical characteristic of the noise plays a crucial role in the success of the brain source recovery process, which can be formulated as a sparse regression problem.

Method

In this study, we assume that the dominant environment and biological sources of noise that have high spatial correlations in the sensors can be expressed as a structured noise model based on the variational Bayesian factor analysis. To the best of our knowledge, no existing algorithm has addressed the brain source estimation problem with such structured noise. We propose to apply a robust empirical Bayesian framework for iteratively estimating the brain source activity and the statistics of the structured noise. In particular, we perform inference of the variational Bayesian factor analysis (VBFA) noise model iteratively in conjunction with source reconstruction.

Results

To demonstrate the effectiveness of the proposed algorithm, we perform experiments on both simulated and real datasets. Our algorithm achieves superior performance as compared to several existing benchmark algorithms.

Discussion

A key aspect of our algorithm is that we do not require any additional baseline measurements to estimate the noise covariance from the sensor data under scenarios such as resting state analysis, and other use cases wherein a noise or artifactual source occurs only in the active period but not in the baseline period (e.g., neuro-modulatory stimulation artifacts and speech movements).

Source localization using recursively applied and projected MUSIC with flexible extent estimation

Magneto- and electroencephalography (M/EEG) are widespread techniques to measure neural activity in-vivo at a high temporal resolution but low spatial resolution. Locating the neural sources underlying the M/EEG poses an inverse problem, which is ill-posed. We developed a new method based on Recursive Application of Multiple Signal Classification (MUSIC). Our proposed method is able to recover not only the locations but, in contrast to other inverse solutions, also the extent of active brain regions flexibly (FLEX-MUSIC). This is achieved by allowing it to search not only for single dipoles but also dipole clusters of increasing extent to find the best fit during each recursion. FLEX-MUSIC achieved the highest accuracy for both single dipole and extended sources compared to all other methods tested. Remarkably, FLEX-MUSIC was capable to accurately estimate the level of sparsity in the source space (r = 0.82), whereas all other approaches tested failed to do so (r ≤ 0.18). The average computation time of FLEX-MUSIC was considerably lower compared to a popular Bayesian approach and comparable to that of another recursive MUSIC approach and eLORETA. FLEX-MUSIC produces only few errors and was capable to reliably estimate the extent of sources. The accuracy and low computation time of FLEX-MUSIC renders it an improved technique to solve M/EEG inverse problems both in neuroscience research and potentially in pre-surgery diagnostic in epilepsy.

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.

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.

Electrophysiological Brain Connectivity: Theory and Implementation

We review the theory and algorithms of electrophysiological brain connectivity analysis. This tutorial is aimed at providing an introduction to brain functional connectivity from electrophysiological signals, including electroencephalography (EEG), magnetoencephalography (MEG), electrocorticography (ECoG), stereoelectroencephalography (SEEG). Various connectivity estimators are discussed, and algorithms introduced. Important issues for estimating and mapping brain functional connectivity with electrophysiology are discussed.

Modified Dominant Mode Rejection Beamformer for Localizing Brain Activities When Data Covariance Matrix Is Rank Deficient

OBJECTIVE

Minimum variance beamformer (MVB) and its extensions fail in localizing short time brain activities particularly evoked potentials because of rank deficiency or inaccurate estimation of a data covariance matrix. In this paper, the conventional dominant mode rejection (DMR) adaptive beamformer is modified to localize brain short time activities.

METHODS

In the modified DMR, it is attempted to obtain a well-conditioned covariance matrix by dividing the eigenvalues of the data covariance matrix into dominant, medium, and small eigenvalues and then modifying medium and small parts. The performance of the proposed approach is compared with diagonal loading MVB (DL_MVB) and fast fully adaptive (FFA) beamformer by using simulated event-related potentials and real event-related field data. Eigenspace versions of DL_MVB and modified DMR are also implemented.

RESULTS

In all simulations, the modified DMR obtains the least localization error (0-5 mm) and spread radius (0-8 mm) when the signal-to-noise ratio (SNR) varies from 0 to 10 dB with step 1 dB. In real data, the new approach in comparison to two other ones attains the most concentrated power spectrum. Eigenspace projection of DL_MVB presents better results than DL_MVB but worse results than the modified DMR. Applying eigenspace projection on the proposed method improves its performance at high SNR levels.

CONCLUSION

Empirical results illustrate the superiority of the proposed DMR method to the DL_MVB and FFA in localizing brain short time activities.

SIGNIFICANCE

The proposed method can be utilized in source localization of epilepsy for presurgical clinical evaluation purpose and also in applications dealing with the localization of evoked potentials and fields.