Simultaneously estimating brain source activity and noise has long been a challenging task in electromagnetic brain imaging using magneto- and electroencephalography. The problem is challenging not only in terms of solving the NP-hard inverse problem of reconstructing unknown brain activity across thousands of voxels from a limited number of sensors, but also for the need to simultaneously estimate the noise and interference. We present a generative model with an augmented leadfield matrix to simultaneously estimate brain source activity and sensor noise statistics in electromagnetic brain imaging (EBI). We then derive three Bayesian inference algorithms for this generative model (expectation-maximization (EBI-EM), convex bounding (EBI-Convex) and fixed-point (EBI-Mackay)) to simultaneously estimate the hyperparameters of the prior distribution for brain source activity and sensor noise. A comprehensive performance evaluation for these three algorithms is performed. Simulations consistently show that the performance of EBI-Convex and EBI-Mackay updates is superior to that of EBI-EM. In contrast to the EBI-EM algorithm, both EBI-Convex and EBI-Mackay updates are quite robust to initialization, and are computationally efficient with fast convergence in the presence of both Gaussian and real brain noise. We also demonstrate that EBI-Convex and EBI-Mackay update algorithms can reconstruct complex brain activity with only a few trials of sensor data, and for resting-state data, achieving significant improvement in source reconstruction and noise learning for electromagnetic brain imaging.

Reconstructing complex brain source activity at a high spatiotemporal resolution from magnetoencephalography (MEG) or electroencephalography (EEG) remains a challenging problem. Adaptive beamformers are routinely deployed for this imaging domain using the sample data covariance. However adaptive beamformers have long been hindered by 1) high degree of correlation between multiple brain sources, and 2) interference and noise embedded in sensor measurements. This study develops a novel framework for minimum variance adaptive beamformers that uses a model data covariance learned from data using a sparse Bayesian learning algorithm (SBL-BF). The learned model data covariance effectively removes influence from correlated brain sources and is robust to noise and interference without the need for baseline measurements. A multiresolution framework for model data covariance computation and parallelization of the beamformer implementation enables efficient high-resolution reconstruction images. Results with both simulations and real datasets indicate that multiple highly correlated sources can be accurately reconstructed, and that interference and noise can be sufficiently suppressed. Reconstructions at 2-2.5mm resolution ( ∼ 150K voxels) are possible with efficient run times of 1-3 minutes. This novel adaptive beamforming algorithm significantly outperforms the state-of-the-art benchmarks. Therefore, SBL-BF provides an effective framework for efficiently reconstructing multiple correlated brain sources with high resolution and robustness to interference and noise.

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.

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 orientation of these sources remains a challenging task, one that is significantly compounded by the effects of source correlations and 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 have theoretically zero bias estimating both the location and orientation of multi-component dipoles even in the presence of correlations, 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.

We have developed a novel algorithm for integrating source localization and noise suppression based on a probabilistic graphical model of stimulus-evoked MEG/EEG data. Our algorithm localizes multiple dipoles while suppressing noise sources with the computational complexity equivalent to a single dipole scan, and is therefore more ef(cid:2)cient than traditional multidipole (cid:2)tting procedures. In simulation, the algorithm can accurately localize and estimate the time course of several simultaneously-active dipoles, with rotating or (cid:2)xed orientation, at noise levels typical for averaged MEG data. Furthermore, the algorithm is superior to beamforming techniques, which we show to be an approximation to our graphical model, in estimation of temporally correlated sources. Success of this algorithm for localizing auditory cortex in a tumor patient and for localizing an epileptic spike source are also demonstrated.

This paper presents a novel technique for analyzing electromagnetic imaging data obtained using the stimulus evoked experimental paradigm. The technique is based on a probabilistic graphical model, which describes the data in terms of underlying evoked and interference sources, and explicitly models the stimulus evoked paradigm. A variational Bayesian EM algorithm infers the model from data, suppresses interference sources, and reconstructs the activity of separated individual brain sources. The new algorithm outperforms existing techniques on two real datasets, as well as on simulated data.

We have developed a method suitable for reconstructing spatio-temporal activities of neural sources using MEG data. Our method is based on an adaptive beamformer technique. It extends a beamformer originally proposed by Borgiotti and Kaplan (1979) to a vector beamformer formulation in which three sets of weight vectors are used to detect the source activity in three orthogonal directions. The weight vectors of this vector-extension of the Borgiotti-Kaplan beamformer are then projected onto the signal subspace of the measurement covariance matrix to obtain a final form of the proposed beamformer's weight vectors. Our numerical experiments demonstrated the effectiveness of the proposed beamformer.

We propose a method that incorporates the time-frequency characteristics of neural sources into magnetoencephalographic (MEG) source estimation. The method is based on the multiple-signal-classification (MUSIC) algorithm and it calculates a time--frequency matrix in which diagonal and off-diagonal terms are the auto and crosstime--frequency distributions of multichannel MEG recordings, respectively. The method averages this time-frequency matrix over the time--frequency region of interest. The locations of neural sources are then estimated by checking the orthogonality between the noise subspace of this averaged matrix and the sensor lead field. Accordingly, the method allows us to estimate the locations of neural sources from each time--frequency component. A computer simulation was performed to test the validity of the proposed method, and the results demonstrate its effectiveness.

External noise fields cause spatially coherent noise in the biomagnetic data measured by a multichannel magnetometer. The authors propose a method of incorporating this spatial coherence into current-density reconstruction. This method can reconstruct current distributions from biomagnetic measurements affected by external noise fields. Computer simulations demonstrate its effectiveness.

The details of the simulated annealing algorithm proposed to estimate the parameters of multiple current dipoles using biomagnetic data are described. The effects of the choices of such numerical conditions as the amount of estimate transitions, the equilibrium criterion, and the temperature decrement on the algorithm's performance are discussed. Incorrect results from the computer simulation obtained with inappropriate choices of such conditions are presented. The verification of a near-optimum convergence by reheating and reannealing is demonstrated. A modification of this algorithm is proposed for implementation by parallel computer, and the validity of this parallel algorithm is demonstrated by computer simulation.