Score-based generative models (SGMs) have recently shown promising results for image reconstruction on simulated positron emission tomography (PET) datasets. In this work we have developed and implemented practical methodology for 3D image reconstruction with SGMs, and perform (to our knowledge) the first SGM-based reconstruction of real fully 3D PET data. We train an SGM on full-count reference brain images, and extend methodology to allow SGM-based reconstructions at very low counts (1% of original, to simulate low-dose or short-duration scanning). We then perform reconstructions for multiple independent realisations of 1% count data, allowing us to analyse the bias and variance characteristics of the method. We sample from the learned posterior distribution of the generative algorithm to calculate uncertainty images for our reconstructions. We evaluate the method's performance on real full- and low-count PET data and compare with conventional OSEM and MAP-EM baselines, showing that our SGM-based low-count reconstructions match full-dose reconstructions more closely and in a bias-variance trade-off comparison, our SGM-reconstructed images have lower variance than existing baselines. Future work will compare to supervised deep-learned methods, with other avenues for investigation including how data conditioning affects the SGM's posterior distribution and the algorithm's performance with different tracers.

翻译：基于分数的生成模型（SGMs）近期在模拟正电子发射断层扫描（PET）数据集上展现出有前景的图像重建效果。本研究开发并实现了基于SGMs的三维图像重建实用方法，并完成了（据我们所知）首个基于SGM的真实完全三维PET数据重建。我们在全计数参考脑部图像上训练SGM，并扩展方法以实现基于SGM的极低计数（原始计数的1%，用于模拟低剂量或短时扫描）重建。随后对多个独立的1%计数数据实例进行重建，从而分析该方法的偏差与方差特性。通过从生成算法学得的后验分布中采样，我们计算了重建结果的不确定性图像。该方法在真实全计数与低计数PET数据上的评估表明：基于SGM的低计数重建结果与全剂量重建结果吻合度更高；在偏差-方差权衡比较中，SGM重建图像相比现有基线方法具有更低的方差。未来工作将对比监督式深度学习方法，其他研究方向包括数据条件如何影响SGM的后验分布，以及算法在不同示踪剂下的性能表现。