Robust Empirical Bayesian Reconstruction of Distributed Sources for Electromagnetic Brain Imaging

Abstract

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.

Fig. 1:

A single MEG simulation example of the localization results with three clusters for six algorithms: Beamformer, sLORETA, MxNE, MSP, Champagne and Smooth Champagne. The ground truth location of clusters are shown for comparison. Only Smooth Champagne captures the true spatial extent of all the sources. In this configuration, the SNR, correlation of dipole activities within the cluster and between clusters are 10 dB, 0.9 and 0.9, respectively.

Fig. 2:

Simulation results of A′ metric with four different configurations. (A) Increasing cluster number; (B) Increasing cluster size; (C) Increasing SNR; (D) Increasing intra-cluster correlation. The results are averaged over 50 simulations at each data point and the error bars show the standard error.

Fig. 3:

Simulation results of the performance of the novel algorithm as a function of local smoothing kernel width and the tile size. We examine performance for reconstruction of 5 clusters of different sizes (from 5–35 voxels per cluster). (A) Results of the performance as a function of increasing the width of the local smoothing kernel from 3 voxels to 121 voxels while the averaged tile size was maintained at 6 voxels. (B) Results of the performance as a function of average tile size ranging from 4–132 voxels per tile while the averaged smoothing kernel size was maintained around 7 voxels. The results are averaged over 50 simulations at each data point and the error bars show the standard error.

Fig. 4:

A single EEG simulation example of the localization results with three clusters for six algorithms: Beamformer, sLORETA, MxNE, MSP, Champagne and Smooth Champagne. The ground truth location of clusters are shown for comparison. In this configuration, the SNR, correlation of dipole activities within the cluster and between clusters are 20 dB, 0.9 and 0.9, respectively.

Fig. 5:

Sensory Evoked Field localization results. All six algorithms localize to somatosensory cortical areas. Here we set the threshold as half of the maximum value.

Fig. 6:

Auditory evoked field (AEF) results with four subjects for six algorithms: Beamformer, sLORETA, MxNE, MSP, Champagne and Smooth Champagne. The results from both Champagne and Smooth Champagne are shown in the last two columns, which outperform the other benchmark algorithms shown in the first to fourth columns.

Fig. 7:

Audio-Visual data localization results from Smooth Champagne. Smooth Champagne is able to localize a bilateral auditory response at 100 ms after the simultaneous presentation of tones and a visual stimulus. For bilateral auditory activity, the results of locations and time courses are shown in (A), (B). Smooth Champagne can localize an early visual response at 150 ms after the simultaneous presentation of tones and visual stimulus shown in (C) and (D).

Fig. 8:

Face processing (EEG) localization results for five algorithms: Beamformer, sLORETA, MxNE, Champagne, and Smooth Champagne. The first row is the average power mapping from 0 ms to 400 ms, the second and third rows are for peak power activity at 100 ms and 170 ms separately.