基于学习的流匹配先验的流形约束PET重建
Manifold-Constrained PET Reconstruction with Learned Flow-Matching Priors
- ZJU-UIUC Institute, Zhejiang University（浙江大学紫金港研究院）
- College of Information Science and Electronic Engineering, Zhejiang University（浙江大学信息与电子工程学院）
- College of Optical Science and Engineering, Zhejiang University（浙江大学光电科学与工程学院）
- Vivo Mobile Communication Co., Ltd.（维沃移动通信有限公司）
- College of Biomedical Engineering and Instrument Science, Zhejiang University（浙江大学生物医学工程与仪器科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究针对PET图像重建的不适定问题，提出一种结合流匹配生成模型先验与乘子交替方向法的无监督优化重建框架，在模拟与真实PET数据集上验证其噪声抑制、结构保留等性能优于传统方法及深度学习基线。
AI中文摘要：
正电子发射断层扫描（PET）的图像重建是一个不适定的泊松逆问题，常面临严重的噪声放大与伪影问题。本研究提出一种无监督、基于优化的重建框架，采用流匹配生成模型作为学习到的流形先验。我们在高质量PET图像上训练流匹配模型，学习从高斯潜在分布到经验PET图像分布的确定性常微分方程传输过程，生成符合解剖结构的可微图像生成器。我们将该生成器作为显式流形约束纳入正则化泊松似然公式，采用乘子交替方向法求解优化问题，其中期望最大化型替代更新保证数据一致性，基于梯度的潜在空间投影确保流形邻近性。我们在模拟和真实PET数据集上评估该方法，测试其剂量水平鲁棒性、病灶插入泛化能力及跨扫描仪迁移性能。与传统重建方法及最先进的深度学习基线相比，所提方法在保持高计算效率的同时，实现了更优的噪声抑制、结构保留及定量准确性。
英文摘要：
Image reconstruction for positron emission tomography (PET) is an ill-posed Poisson inverse problem that often suffers from severe noise amplification and artifacts. In this work, we introduce an unsupervised, optimization-based reconstruction framework that employs a flow-matching generative model as a learned manifold prior. We train the flow-matching model on high-quality PET images to learn a deterministic ordinary differential equation transport from a Gaussian latent distribution to the empirical PET image distribution, yielding a differentiable generator of anatomically plausible images. We incorporate this generator as an explicit manifold constraint into a regularized Poisson likelihood formulation. We solve the resulting optimization problem using an alternating direction method of multipliers algorithm, in which an expectation-maximization-type surrogate update enforces data consistency and a gradient-based latent-space projection enforces manifold proximity. We evaluate the proposed method on both simulated and real PET datasets, assessing dose-level robustness, lesion-insertion generalization, and cross-scanner transfer. Compared with conventional reconstruction methods and state-of-the-art deep learning baselines, the proposed method provides superior noise suppression, structural preservation, and quantitative accuracy, while maintaining high computational efficiency.
