Incomplete Computed Tomography (CT) benefits patients by reducing radiation exposure. However, reconstructing high-fidelity images from limited views or angles remains challenging due to the ill-posed nature of the problem. Deep Learning Reconstruction (DLR) methods have shown promise in enhancing image quality, but the paradox between training data diversity and high generalization ability remains unsolved. In this paper, we propose a novel Gaussian Representation for Incomplete CT Reconstruction (GRCT) without the usage of any neural networks or full-dose CT data. Specifically, we model the 3D volume as a set of learnable Gaussians, which are optimized directly from the incomplete sinogram. Our method can be applied to multiple views and angles without changing the architecture. Additionally, we propose a differentiable Fast CT Reconstruction method for efficient clinical usage. Extensive experiments on multiple datasets and settings demonstrate significant improvements in reconstruction quality metrics and high efficiency. We plan to release our code as open-source.

翻译：不完整计算机断层扫描（CT）通过减少辐射暴露使患者受益。然而，由于问题的病态性质，从有限视角或角度重建高保真图像仍然具有挑战性。深度学习重建（DLR）方法在提升图像质量方面显示出潜力，但训练数据多样性与高泛化能力之间的悖论仍未解决。本文提出了一种无需使用任何神经网络或全剂量CT数据的新型高斯表示方法，用于不完整CT重建（GRCT）。具体而言，我们将三维体建模为一组可学习的高斯分布，这些分布直接从不完整的正弦图中优化得到。我们的方法可适用于多种视角和角度，而无需改变架构。此外，我们提出了一种可微分的快速CT重建方法，以实现高效的临床应用。在多个数据集和设置上的大量实验表明，该方法在重建质量指标和效率方面均有显著提升。我们计划将代码开源发布。