标题： 通过最优传输的组级MEG/EEG源成像：最小Wasserstein估计 显示英文标题

标题： Group level MEG/EEG source imaging via optimal transport: minimum Wasserstein estimates

摘要： 脑磁图（MEG）和脑电图（EEG）是无创的模态，用于测量由神经活动产生的微弱电磁场。 推断产生这些磁场的电流源的位置是一个病态的逆问题，称为源成像。 在考虑群体研究时，一种基线方法是为每个受试者独立进行这些源的估计。 每个问题的病态性通常通过促进稀疏性的正则化来解决。 然后，定义这些源的共同模式的一种直接方法是对其进行平均。 一种更高级的替代方法是通过在所有受试者的估计源之间强制某种相似性，来进行所有受试者的联合定位。 这种方法的一个重要优势是它是一个单一的估计过程，在此过程中所有测量数据都被合并在一起，从而使逆问题更适定。 然而，这种联合估计带来了一些挑战，特别是选择一个可以量化这种空间相似性的有效正则化器。 在这项工作中，我们提出了一种新的程序，可以在考虑皮层几何结构的同时做到这一点。 我们将这个过程称为最小Wasserstein估计（MWE）。 该模型的好处有两个。 首先，联合推断允许将不同脑几何的数据合并在一起，积累更多的空间信息。 其次，MWE是通过最优传输（OT）度量定义的，这提供了一种工具来建模不同受试者的皮层源之间的空间接近性，因此并不强制组内相同的源位置。 这些好处使得MWE比标准的MEG源定位技术更准确。 为了支持这些说法，我们在基于MRI扫描导出的前向算子的现实MEG模拟上进行了源定位。 在一个视觉任务数据集上，我们展示了MWE如何推断出与功能性磁共振成像（fMRI）图相似的神经模式。 显示英文摘要

摘要： Magnetoencephalography (MEG) and electroencephalogra-phy (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.