Group Level MEG/EEG Source Imaging via Optimal Transport: Minimum Wasserstein Estimates

Abstract

Magnetoencephalography (MEG) and electroencephalography (EEG) are non-invasive modalities that measure the weak electromagnetic fields generated by neural activity. Inferring the location of the current sources that generated these magnetic fields is an ill-posed inverse problem known as source imaging. When considering a group study, a baseline approach consists in carrying out the estimation of these sources independently for each subject. The ill-posedness of each problem is typically addressed using sparsity promoting regularizations. A straightforward way to define a common pattern for these sources is then to average them. A more advanced alternative relies on a joint localization of sources for all subjects taken together, by enforcing some similarity across all estimated sources. An important advantage of this approach is that it consists in a single estimation in which all measurements are pooled together, making the inverse problem better posed. Such a joint estimation poses however a few challenges, notably the selection of a valid regularizer that can quantify such spatial similarities. We propose in this work a new procedure that can do so while taking into account the geometrical structure of the cortex. We call this procedure Minimum Wasserstein Estimates (MWE). The benefits of this model are twofold. First, joint inference allows to pool together the data of different brain geometries, accumulating more spatial information. Second, MWE are defined through Optimal Transport (OT) metrics which provide a tool to model spatial proximity between cortical sources of different subjects, hence not enforcing identical source location in the group. These benefits allow MWE to be more accurate than standard MEG source localization techniques. To support these claims, we perform source localization on realistic MEG simulations based on forward operators derived from MRI scans. On a visual task dataset, we demonstrate how MWE infer neural patterns similar to functional Magnetic Resonance Imaging (fMRI) maps.

An Optimal Transport Based Transferable System for Detection of Erroneous Somato-Sensory Feedback from Neural Signals

“…In our future studies, we will first aim to improve the existing transferable framework including unsupervised training to design a more robust and adaptable ErrP decoder. This framework has been tested for only this problem, but results from our present study and previous studies [ 47 , 48 , 49 ] shows the efficiency of implementing optimal transport for transferable EEG decoding. Nevertheless, we will continue testing our transferable error detection approach in more motor-related, cognitive and behavioural experiments so that we can develop a more generalised error detection framework.…”

“…In this study, we apply optimal transport theory [ 46 ] as a transfer learning technique to train a classifier on erroneous and correct trials for a known group of users and to test it on an unknown user (cross-subject). An optimal transport was previously used in source localization using an EEG/MEG [ 47 ], P300 [ 48 ], and sleep stage detection [ 49 ], although this is the first time it is being used for error detection.…”

Unification of Sparse Bayesian Learning Algorithms for Electromagnetic Brain Imaging with the Majorization Minimization Framework

“…We have provided a unifying theoretical platform for deriving different sparse Bayesian learning algorithms for electromagnetic brain imaging using the Majorization-Minimization (MM) framework. [86], Rényi [87], Itakura-Saito (IS) [88], [89] and β divergences [90]- [94] as well as transportation metrics such as the Wasserstein distance between empirical and statistical covariances (e.g., [95]- [98]).…”

Multi-subject MEG/EEG source imaging with sparse multi-task regression

“…To alleviate this problem, one can infer both the sources and the noise variance for each subject and scale the regularization according to the level of noise. Following similar ideas that lead to the concomitant Lasso [46,51,58] or the multi-task Lasso [43], the Minimum Wasserstein Estimates (MWE) was first proposed in [31]. However both MTW and MWE rely on convex 1 norm penalties which tend to promote sparse solutions at the expense of an amplitude bias.…”

“…A preliminary version of this work was presented at the international conference on Information Processing in Medical Imaging (IPMI) [31].…”