Bayesian PET Reconstruction with Learned Flow Matching Priors via Langevin Sampling

Generative models have shown strong potential for positron emission tomography (PET) image reconstruction. Although diffusion model-based reconstruction methods have demonstrated promising performance, they often require many reverse sampling steps with data-consistency updates incorporated into the sampling process. Flow matching offers an attractive alternative because it can directly estimate clean images from intermediate states, allowing data-consistency refinement to be separated from flow propagation. In this work, we proposed flow matching-based PET image reconstruction methods. We first established PET-FlowDPS by incorporating Poisson likelihood guidance with an expectation-maximization (EM)-based preconditioner into the FlowDPS framework. We then proposed a model-based PET reconstruction method that used a pretrained flow matching model as a prior, in which the flow-based prior, PET data refinement, and stochastic propagation were interpreted within an approximate Bayesian framework. Experimental results using [$^{\text{18}}\text{F}$]FDG brain PET datasets showed that the proposed method achieved better bias-variance trade-offs across different dose levels compared with other reference methods. These results demonstrated the potential of flow matching as a generative prior for quantitative PET image reconstruction.

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 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 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.

Positron Emission Tomography (PET) image reconstruction is inherently challenged by Poisson noise and physical degradation factors, which are further exacerbated in limited-angle acquisitions. While deep learning methods demonstrate promising performance, their generalization to unseen clinical data distributions remains limited without extensive retraining. We propose PET-Adapter, a test-time domain adaptation framework for generative PET reconstruction models pretrained solely on phantom data. Our method enables adaptation to clinical datasets with varying anatomies, tracers, and scanner configurations without requiring paired ground truth. PET-Adapter introduces layer-wise low-rank anatomical conditioning during adaptation and Ordered Subset Expectation Maximization-based warm-starting that initializes the generation from physics-informed reconstructions, reducing diffusion steps from 50 to 2 without compromising quality. Experiments across multiple clinical datasets demonstrate superior 3D reconstruction performance in both full-angle and limited-angle settings, highlighting the clinical feasibility and computational efficiency of the proposed approach.