通过最佳传输的组级MEG/EEG源成像：最小Wasserstein估计
Group level MEG/EEG source imaging via optimal transport: minimum Wasserstein estimates
摘要：
脑磁图（MEG）和脑电图（EEG）是测量神经活动产生的弱电磁场的非侵入性方式。推断产生这些磁场的电流源的位置是一个不适定的逆问题，称为源成像。当考虑一组研究时，基线方法包括对每个受试者独立地进行这些来源的估计。每个问题的不适定性通常使用稀疏促进正则化来解决。为这些源定义共同模式的一种直接方法是对它们进行平均。一个更先进的替代方案依赖于联合本地化的来源，为所有科目一起采取，通过强制执行一些相似性，所有估计的来源。这种方法的一个重要优点是，它包括在一个单一的估计，其中所有的测量汇集在一起，使逆问题更好地提出。然而，这样的联合估计提出了一些挑战，特别是选择一个有效的正则化，可以量化这种空间相似性。在这项工作中，我们提出了一个新的程序，可以做到这一点，同时考虑到皮质的几何结构。我们称这个过程为最小Wasserstein估计（MWE）。这种模式的好处是双重的。首先，联合推理允许将不同大脑几何形状的数据汇集在一起，积累更多的空间信息。第二，MWE定义通过最佳运输（OT）指标，提供了一种工具，以模拟不同科目的皮质源之间的空间接近度，因此不强制相同的源位置组。这些优点使得MWE比标准的MEG源定位技术更准确。为了支持这些说法，我们进行源定位现实的MEG模拟的基础上，来自MRI扫描的前向运营商。在视觉任务数据集上，我们演示了MWE如何推断类似于功能磁共振成像（fMRI）地图的神经模式。
英文摘要：
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.
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