发表机构
Centre for Smart Health, The Hong Kong Polytechnic University, Hong Kong, China; Department of Nuclear Medicine, Sun Yat-sen University Cancer Center, Guangzhou, China; Research Center for Medical AI, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China（智能健康研究中心，香港理工大学，中国香港; 核医学部，中山大学肿瘤中心，中国广州; 医学人工智能研究中心，深圳先进技术研究院，中国科学院，中国深圳）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对低计数PET重建难题，提出FlowPET框架，通过可分离哈密顿系统参数化后验动力学，引入共轭边界条件，经辛流匹配训练和辛蛙跳积分器推理，实验证明其在指标上超基线，能更好恢复低对比度病变。
AI 中文摘要
低计数正电子发射断层扫描（PET）重建受到现有生成模型耗散性质的严重阻碍，其固有的相空间收缩会导致微弱但具有诊断关键意义的病变信号在数值上消失（“洗脱”）。为克服这一几何限制，我们提出了FlowPET，这是一个物理信息框架，将重建重新表述为辛相空间中的体积守恒传输。通过可分离哈密顿系统对后验动力学进行参数化，我们的方法从理论上保证了无散度向量场，使微弱信号免受概率质量坍塌的影响。为引导这种保守流，我们基于PET算子的值域-零空间分解引入共轭边界条件，严格强制值域空间中的数据一致性，同时将随机不确定性注入限制在未观测的零空间。我们通过辛流匹配训练模型，并使用辛蛙跳积分器进行推理。在BrainWeb、临床儿科和UDPET数据集上的大量实验表明，FlowPET不仅在结构相似性指数（SSIM）和峰值信噪比（PSNR）方面超越了现有最先进的确定性和随机基线，更关键的是，它在低对比度病变的恢复方面表现出色。结果证实，施加哈密顿结构约束为高噪声环境下的医学逆问题提供了强大的几何保障。
英文摘要
Low-count Positron Emission Tomography (PET) reconstruction is severely hindered by the dissipative nature of prevailing generative models, where the inherent phase-space contraction leads to the numerical extinction (``wash-out'') of weak but diagnostically critical lesion signals. To overcome this geometric limitation, we propose \textbf{FlowPET}, a physics-informed framework that reformulates reconstruction as volume-preserving transport in a symplectic phase space. By parameterizing the posterior dynamics via a Separable Hamiltonian System, our approach guarantees a divergence-free vector field by construction, theoretically immunizing weak signals against probability mass collapse. To steer this conservative flow, we introduce conjugate boundary conditions based on the Range-Null space decomposition of the PET operator; this strictly enforces data consistency in the range space while confining stochastic uncertainty injection to the unobserved null space. We train the model via symplectic flow matching and perform inference using a symplectic leapfrog integrator. Extensive experiments on BrainWeb, clinical pediatric, and UDPET datasets demonstrate that \textbf{FlowPET} not only surpasses state-of-the-art deterministic and stochastic baselines in SSIM and PSNR but, more crucially, exhibits superior recovery of low-contrast lesions. The results confirm that imposing Hamiltonian structural constraints offers a robust geometric safeguard for medical inverse problems in high-noise regimes.
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