Distribution matching based personalized federated learning for multi-center, cross-modal liver image registration

In clinical liver MRI, diffusion-weighted imaging (DWI) and dynamic contrast-enhanced (DCE) imaging are commonly used and complementary sequences, particularly for liver tumor diagnosis and assessment. Accurate registration between the two modalities facilitates subsequent quantitative analysis and multi-modal image-based evaluation. Although deep learning has achieved remarkable progress in image registration, considerable challenges remain in multi-parametric liver imaging, mainly due to substantial contrast differences, pronounced respiratory motion, limited single-center training data, and inter-center heterogeneity. This study proposes a cross-modal registration framework for liver DWI and DCE across multi-center datasets. First, a multi-task synthesis-registration network (SynReg) is introduced, which integrates image synthesis and registration within a unified architecture to reduce cross-modal appearance discrepancy and facilitate deformable registration. To further improve personalized learning under cross-center heterogeneity, we propose a personalized decentralized distribution matching (PDDM) framework with SynReg as the backbone. PDDM performs compatibility-aware selective collaboration by identifying compatible external training cases and constructing client-specific collaboration relationships. Signal-to-noise ratio (SNR) distributions are used as a lightweight compatibility descriptor, while the synthesis components remain local and the registration network is selectively aggregated among compatible clients. The framework was evaluated on six datasets collected from five medical centers and acquired on MRI systems from three vendors under both low- and high-b-value settings. PDDM consistently achieved more favorable registration performance than single-center training and representative personalized federated learning methods, while remaining closely competitive with centralized pooled-data training. In comparisons with alternative matching strategies, PDDM showed the most consistently favorable overall performance across centers, b-value settings, and registration metrics. These findings support compatibility-aware selective collaboration as an effective strategy for personalized multi-center liver image registration. Code will be available at https://github.com/ZIC-skyzrc/PDDM-SynReg.