Positron emission tomography (PET) reconstruction is a critical challenge in molecular imaging, often hampered by noise amplification, structural blurring, and detail loss due to sparse sampling and the ill-posed nature of inverse problems. The three-dimensional discrete Gaussian representation (GR), which efficiently encodes 3D scenes using parameterized discrete Gaussian distributions, has shown promise in computer vision. In this work, we pro-pose a novel GR-Diffusion framework that synergistically integrates the geometric priors of GR with the generative power of diffusion models for 3D low-dose whole-body PET reconstruction. GR-Diffusion employs GR to generate a reference 3D PET image from projection data, establishing a physically grounded and structurally explicit benchmark that overcomes the low-pass limitations of conventional point-based or voxel-based methods. This reference image serves as a dual guide during the diffusion process, ensuring both global consistency and local accuracy. Specifically, we employ a hierarchical guidance mechanism based on the GR reference. Fine-grained guidance leverages differences to refine local details, while coarse-grained guidance uses multi-scale difference maps to correct deviations. This strategy allows the diffusion model to sequentially integrate the strong geometric prior from GR and recover sub-voxel information. Experimental results on the UDPET and Clinical datasets with varying dose levels show that GR-Diffusion outperforms state-of-the-art methods in enhancing 3D whole-body PET image quality and preserving physiological details.

翻译：正电子发射断层扫描（PET）重建是分子成像领域的一项关键挑战，常因稀疏采样及逆问题的不适定性而受到噪声放大、结构模糊和细节丢失的困扰。三维离散高斯表示（GR）通过参数化的离散高斯分布高效编码三维场景，已在计算机视觉领域展现出潜力。本文提出一种新颖的GR-Diffusion框架，将GR的几何先验与扩散模型的生成能力协同整合，用于三维低剂量全身体部PET重建。GR-Diffusion利用GR从投影数据生成参考三维PET图像，建立起物理基础扎实且结构显式的基准，克服了传统基于点或基于体素方法的低通限制。该参考图像在扩散过程中发挥双重引导作用，确保全局一致性与局部精确性。具体而言，我们采用基于GR参考的分层引导机制：细粒度引导利用差异图优化局部细节，粗粒度引导则通过多尺度差异图校正偏差。该策略使扩散模型能够顺序整合来自GR的强几何先验，并恢复亚体素级信息。在UDPET和临床数据集上对不同剂量水平进行的实验表明，GR-Diffusion在提升三维全身体部PET图像质量与保留生理细节方面均优于现有先进方法。