传感器几何作为多通道脑信号的流匹配先验

中文摘要 AI 辅助

流匹配模型从各向同性高斯源开始，这是当数据相关结构事先未知时的标准选择。然而，对于多通道脑记录，部分结构是事先已知的。电极位于头部的固定位置，通过颅骨和头皮的容积传导使得邻近电极的协变方式在受试者之间共享。现有的脑电生成模型仍然让网络从头学习这种结构。我们将这种结构放入源中。仅从传感器坐标出发，我们构建一个k近邻图，并取其拉普拉斯算子的图-Matérn函数作为源协方差，因此流从空间相干模式而非通道独立噪声开始。这一改变不增加任何可学习参数，适用于任何耦合和任何漂移网络，并在每个数据集上使用相同的三个超参数。在八个脑电数据集和四种流匹配方法中，图-Matérn源在大多数数据集上降低了生成信号与真实信号在五个临床频带中的谱差异（PSD-KL）。PSD-KL在数据集上的几何平均下降12%至17%，具体取决于方法，在密度最高的PhysioNet-MI上下降高达40%。我们证明，这种改进源于传感器位置局部图的空间特征向量，因为随机化特征向量同时保留特征值谱会消除增益。此外，直接拟合经验数据协方差的先验表现不如各向同性噪声。相同的构造可不变地应用于MEG、具有患者特定网格的颅内脑电以及交通传感器网络，在每种方法上均降低了PSD-KL。

英文摘要

Flow-matching models start from an isotropic Gaussian source, the standard choice when the correlation structure of the data is unknown in advance. For multi-channel brain recordings, however, part of this structure is known in advance. Electrodes sit at fixed positions on the head, and volume conduction through the skull and scalp makes nearby electrodes co-vary in a way that is shared across subjects. Existing EEG generative models nonetheless leave the network to learn this from scratch. We put this structure into the source instead. From the sensor coordinates alone, we build a k-nearest-neighbor graph and take a graph-Matérn function of its Laplacian as the source covariance, so the flow starts from spatially coherent patterns rather than channel-independent noise. The change adds no learned parameters, works with any coupling and any drift network, and uses the same three hyperparameters on every dataset. Across eight EEG datasets and four flow-matching methods, the graph-Matérn source lowers the spectral discrepancy between generated and real signals in the five clinical bands (PSD-KL) on most datasets. PSD-KL falls by 12% to 17% in geometric mean over datasets depending on the method and by up to 40% on PhysioNet-MI, the densest montage. We show that the improvement stems from the spatial eigenvectors of the local graph of sensor positions, since randomizing the eigenvectors while preserving the eigenvalue spectrum eliminates the gain. Furthermore, a prior fitted directly to the empirical data covariance performs worse than isotropic noise. The same construction applies unchanged to MEG, intracranial EEG with patient-specific grids, and a traffic-sensor network, lowering PSD-KL for every method on each. https://jd730.github.io/projects/GraphPrior

发表机构

• Massachusetts Institute of Technology（麻省理工学院）

机构由 AI 辅助整理，请以论文原文为准。