3D Gaussian splatting (3DGS) has shown promising results in image rendering and surface reconstruction. However, its potential in volumetric reconstruction tasks, such as X-ray computed tomography, remains under-explored. This paper introduces R2-Gaussian, the first 3DGS-based framework for sparse-view tomographic reconstruction. By carefully deriving X-ray rasterization functions, we discover a previously unknown integration bias in the standard 3DGS formulation, which hampers accurate volume retrieval. To address this issue, we propose a novel rectification technique via refactoring the projection from 3D to 2D Gaussians. Our new method presents three key innovations: (1) introducing tailored Gaussian kernels, (2) extending rasterization to X-ray imaging, and (3) developing a CUDA-based differentiable voxelizer. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches by 0.93 dB in PSNR and 0.014 in SSIM. Crucially, it delivers high-quality results in 3 minutes, which is 12x faster than NeRF-based methods and on par with traditional algorithms. The superior performance and rapid convergence of our method highlight its practical value.

翻译：三维高斯溅射（3DGS）在图像渲染和表面重建方面已展现出有前景的结果。然而，其在体绘制重建任务（如X射线计算机断层扫描）中的潜力仍未得到充分探索。本文提出了R2-Gaussian，这是首个基于3DGS的稀疏视角断层扫描重建框架。通过严谨推导X射线光栅化函数，我们发现了标准3DGS公式中一个先前未知的积分偏差，该偏差阻碍了精确的体积信息恢复。为解决此问题，我们通过重构从3D到2D高斯分布的投影，提出了一种新颖的校正技术。我们的新方法包含三个关键创新：（1）引入定制化的高斯核函数，（2）将光栅化扩展至X射线成像领域，（3）开发了基于CUDA的可微分体素化器。大量实验表明，我们的方法在PSNR指标上优于现有最佳方法0.93 dB，在SSIM指标上优于0.014。更重要的是，该方法能在3分钟内生成高质量结果，比基于NeRF的方法快12倍，并与传统算法速度相当。我们方法所展现的卓越性能和快速收敛特性凸显了其实用价值。