Feynman Kac Reweighted Schr"odinger Bridge Matching for Surface-Based Tau PET Harmonization

Tau positron emission tomography (PET) is widely used for the in vivo characterization of disease stage and progression in Alzheimer's disease (AD). With the adoption of multiple tau PET tracers including AV-1451, PI-2620, MK-6240 with different binding behaviors in various large-scale studies, there is a great need of effective harmonization methods to enable the cross-tracer integration of tau PET datasets. While previous methods such as CenTauR were proposed to standardize scalar tau PET measures, they are limited in accounting for the heterogeneity of tau pathology. In this work, we propose Feynman-Kac Reweighted Schr"odinger Bridge Matching (FKRSBM), a surface-based framework for cross-tracer tau PET harmonization. FKRSBM learns a direct stochastic transport between tracer domains using Schr"odinger Bridge matching, avoiding the Gaussian-prior routing used in diffusion-based translation. To promote biologically consistent transport, FKRSBM introduces an endpoint penalty favoring bridge pairings with matched tau-pathology status and implements it through a Feynman-Kac reweighted endpoint proposal. To preserve cortical organization, FKRSBM uses a spherical convolutional network for vertex-level harmonization on cortical surface meshes. In our experiments, we demonstrate our method by harmonizing Tau PET images acquired with the AV-1451 (n=1480) and PI-2620 (n=2458) tracers from two large-scale datasets. Compared to previous methods including ComBat, CycleGAN, Diffusion Model(DF), and unregularized Schr"odinger Bridge Model(DSBM), the proposed FKRSBM method outperforms these baselines in subgroup-level alignment, tau-positivity consistency, and diagnostic classification while preserving subject-specific cortical topography of tau pathology. The code is available at: https://github.com/jianweizhang17/FKRSBM.