Tau PET imaging is central to tracking Alzheimer's disease progression, but systematic differences between scanners, protocols, and radiotracers across sites introduce nonbiological variability that inflates biomarker variance, reduces sensitivity to disease effects, and can bias downstream clinical assessments. Harmonization methods aim to remove these site-induced shifts while preserving biologically meaningful signal, yet existing approaches struggle when source and target cohorts differ in subgroup composition, risking conflation of site effects with biological variation such as tau-positivity status. We propose the Feynman Kac Reweighted Schröodinger Bridge Matching (FKRSBM) model to address this problem. Rather than routing data through a Gaussian noise prior as in diffusion-based methods, FKRSBM learns a direct stochastic transport process between source and target distributions via entropy-regularized optimal transport. To enforce biologically consistent transport, FKRSBM incorporates a subgroup-aware endpoint proposal derived from a Feynman Kac reweighting of the reference bridge measure, implemented entirely through stratified importance sampling at the data level and requiring no changes to the underlying bridge-matching solver or network architecture. For surface-based neuroimaging, FKRSBM employs a spherical convolutional backbone operating on cortical meshes to perform vertex-level harmonization. We evaluate the method on tau PET SUVR maps, harmonizing PI-2620 data from the HABS-HD cohort into the AV-1451 domain of ADNI. Compared against ComBat, CycleGAN, a diffusion-based method (DF), and unregularized Diffusion Schröodinger Bridge Matching (DSBM), FKRSBM achieves superior distributional alignment, reduced tau-positivity sign mismatch, stronger APOE subgroup alignment, and improved downstream disease classification performance.

翻译：Tau PET成像在追踪阿尔茨海默病进展中至关重要，但不同扫描设备、采集协议及影像示踪剂间的系统性差异会引入非生物变异性，导致生物标志物方差膨胀、对疾病效应的敏感性降低，并可能使下游临床评估产生偏差。归一化方法旨在消除这些由数据采集中心引入的偏移，同时保留具有生物学意义的信号，然而现有方法在源域与目标域队列存在亚组构成差异时面临挑战，易将中心效应与诸如tau阳性状态等生物学变异混淆。为解决该问题，我们提出费曼-卡克重加权薛定谔桥匹配（FKRSBM）模型。与基于扩散方法需通过高斯噪声先验传递数据不同，FKRSBM通过熵正则化最优传输学习源域与目标域分布间的直接随机传输过程。为保证生物学上一致的传输，FKRSBM引入基于费曼-卡克重加权参考桥测度的亚组感知端点提议机制，该机制完全通过数据层面的分层重要性采样实现，无需修改底层桥匹配求解器或网络架构。针对基于表面的神经影像，FKRSBM采用作用于皮层网格的球形卷积主干架构进行顶点级归一化。我们在tau PET SUVR图像上评估该方法，将HABS-HD队列的PI-2620数据归一化至ADNI研究的AV1451域。与ComBat、CycleGAN、基于扩散的方法（DF）及无正则化扩散薛定谔桥匹配（DSBM）相比，FKRSBM在分布对齐、tau阳性符号不匹配减少、APOE亚组对齐强度及下游疾病分类性能方面均表现更优。