[1910.01914v1] Multi-subject MEG/EEG source imaging with sparse multi-task regression
As seen in Figure 7, activation foci in x̄ are well limited to primary auditory cortices while solvers that are not based on a group-level multi-task regression model lead to spurious activations next to secondary somatosensory cortices and on middle temporal gyrus

\begin{abstract}
Magnetoencephalography and electroencephalography (M/EEG) are non-invasive modalities that measure the weak electromagnetic fields generated by neural activity. Estimating the location and magnitude of the current sources that generated these electromagnetic fields is a challenging ill-posed regression problem known as \emph{source imaging}. When considering a group study, a common approach consists in carrying out the regression tasks independently for each subject. An alternative is to jointly localize sources for all subjects taken together, while enforcing some similarity between them. By pooling all measurements in a single multi-task regression, one makes the problem better posed, offering the ability to identify more sources and with greater precision. The Minimum Wasserstein Estimates (MWE) promotes focal activations that do not perfectly overlap for all subjects, thanks to a regularizer based on Optimal Transport (OT) metrics. MWE promotes spatial proximity on the cortical mantel while coping with the varying noise levels across subjects.
On realistic simulations, MWE decreases the localization error by up to 4 mm per source compared to individual solutions. Experiments on the Cam-CAN dataset show a considerable improvement in spatial specificity in population imaging.
Our analysis of a multimodal dataset shows how multi-subject source localization closes the gap between MEG and fMRI for brain mapping.
\end{abstract}
‹

Fig. 1. Levels of the W distance in cm (a.k.a Earth mover distance) computed between a fixed blurred activation a (green) and all focal activations b of the triangular mesh of the cortex. Left: Medial view. Right: Lateral view. (Optimal transport background)Fig. 2. Illustration of the Wasserstein barycenter x̄ (middle) of 5 activations inputs x(s) (left) with random amplitudes between 20 and 30 nAm in the middle and occipital lunatus sulcus defined by the aparc.a2009s segmentation. x̄ is located at the average location of the inputs with an average amplitude levels. The Euclidean barycenter (right) is the usual mean: it creates undesirable blurring. (Optimal transport background)Fig. 3. Example of a simulated source configuration with 5 activations for S = 6 subjects one activation per label. The 5 labels – highlighted within green borders – are taken from the aparc.a2009s FreeSurfer Destrieux parcellation [13]. Different radii are used to distinguish overlapping sources. Here, subjects 1, 3 and 5 share the exact same source locations. (Experiments)Fig. 4. Performance of different models over 30 trials in terms of AUC, EMD and MSE using the same leadfield for all subjects (randomly selected in each trial) (left) and different leadfields (right) computed using Cam-CAN dataset with 5 simulated sources. (Experiments)

Fig. 5. Number of active sources for MWE models with λ = 30%. The mean is reported across all subjects. With reweighted MWE, a similar phase transition occurs for both datasets after a certain µmax. (Experiments on MEG data)Fig. 6. Support of source estimates of MWE0.5 recovered in the auditory task of Cam-CAN with 32 subjects (top) and the visual task of DS117 with 16 subjects (bottom). Each color corresponds to a subject. Different radii are displayed for a better distinction of sources. Increasing µ with µ < µmax promotes functional consistency across subjects. Top: Cam-CAN dataset (λ = 30%). Bottom: DS117 dataset (λ = 20%). (Experiments on MEG data)Fig. 7. Average source estimates of different solvers. Top: Cam-CAN dataset. Bottom: DS117 dataset. MWE0.5 x̄ is the latent variable inferred in the MWE0.5 model, corresponding to a Wasserstein barycenter of the MWE0.5 source estimates. MWE0.5 reduces blurring by promoting functional consistency. (Experiments on MEG data)Fig. 8. Mean geodesic distance between the mode of the M/EEG derived neural activation map and the vertices of the labels FFA and V1. Each dot represents one of the 16 subjects. For some subjects, MCE / reweighted MCE produce 6-sparse solutions entirely in the right hemisphere, to which the goedesic +∞ is assigned. (Experiments on MEG data)