# R2-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction

arXiv: https://arxiv.org/abs/2405.20693 · HTML: https://mlsanity.com/paper/2405.20693/

## Key facts

- Cited by 67 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 68 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 30 of 31)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [DreamGaussian: Generative Gaussian Splatting for Efficient 3D Content Creation](https://mlsanity.com/paper/2309.16653/) (2023)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [Scaffold-GS: Structured 3D Gaussians for View-Adaptive Rendering](https://mlsanity.com/paper/2312.00109/) (2023)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Text-to-3D using Gaussian Splatting](https://mlsanity.com/paper/2309.16585/) (2023)
- [GaussianDreamer: Fast Generation from Text to 3D Gaussians by Bridging 2D and 3D Diffusion Models](https://mlsanity.com/paper/2310.08529/) (2023)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [GS-IR: 3D Gaussian Splatting for Inverse Rendering](https://mlsanity.com/paper/2311.16473/) (2023)
- [Gaussian-Flow: 4D Reconstruction with Dynamic 3D Gaussian Particle](https://mlsanity.com/paper/2312.03431/) (2023)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [NeuSG: Neural Implicit Surface Reconstruction with 3D Gaussian Splatting Guidance](https://mlsanity.com/paper/2312.00846/) (2023)
- [Solving 3D Inverse Problems using Pre-trained 2D Diffusion Models](https://mlsanity.com/paper/2211.10655/) (2022)
- [Pixel-GS: Density Control with Pixel-aware Gradient for 3D Gaussian Splatting](https://mlsanity.com/paper/2403.15530/) (2024)
- [NAF: Neural Attenuation Fields for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2209.14540/) (2022)
- [HumanGaussian: Text-Driven 3D Human Generation with Gaussian Splatting](https://mlsanity.com/paper/2311.17061/) (2023)
- [X2CT-GAN: Reconstructing CT from Biplanar X-Rays with Generative Adversarial Networks](https://mlsanity.com/paper/1905.06902/) (2019)
- [DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstruction](https://mlsanity.com/paper/2211.12340/) (2022)
- [Structure-Aware Sparse-View X-ray 3D Reconstruction](https://mlsanity.com/paper/2311.10959/) (2023)
- [Radiative Gaussian Splatting for Efficient X-ray Novel View Synthesis](https://mlsanity.com/paper/2403.04116/) (2024)
- [Improving 3D Imaging with Pre-Trained Perpendicular 2D Diffusion Models](https://mlsanity.com/paper/2303.08440/) (2023)
- [Learning Deep Intensity Field for Extremely Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2303.06681/) (2023)
- [Lose The Views: Limited Angle CT Reconstruction via Implicit Sinogram Completion](https://mlsanity.com/paper/1711.10388/) (2017)
- [TomoGAN: Low-Dose Synchrotron X-Ray Tomography with Generative Adversarial Networks](https://mlsanity.com/paper/1902.07582/) (2019)
- [3DGR-CT: Sparse-View CT Reconstruction with a 3D Gaussian Representation](https://mlsanity.com/paper/2312.15676/) (2023)

## Built on by (most cited first, 30 of 67)

- [Volumetrically Consistent 3D Gaussian Rasterization](https://mlsanity.com/paper/2412.03378/) (2024)
- [UltraGauss: Ultrafast Gaussian Reconstruction of 3D Ultrasound Volumes](https://mlsanity.com/paper/2505.05643/) (2025)
- [Discretized Gaussian Representation for Tomographic Reconstruction](https://mlsanity.com/paper/2411.04844/) (2024)
- [X-LRM: X-ray Large Reconstruction Model for Extremely Sparse-View Computed Tomography Recovery in One Second](https://mlsanity.com/paper/2503.06382/) (2025)
- [X2-Gaussian: 4D Radiative Gaussian Splatting for Continuous-time Tomographic Reconstruction](https://mlsanity.com/paper/2503.21779/) (2025)
- [X-GRM: Large Gaussian Reconstruction Model for Sparse-view X-rays to Computed Tomography](https://mlsanity.com/paper/2505.15235/) (2025)
- [Are Pixel-Wise Metrics Reliable for Sparse-View Computed Tomography Reconstruction?](https://mlsanity.com/paper/2506.02093/) (2025)
- [From Coarse to Fine: Learnable Discrete Wavelet Transforms for Efficient 3D Gaussian Splatting](https://mlsanity.com/paper/2506.23042/) (2025)
- [DeepSparse: A Foundation Model for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2505.02628/) (2025)
- [GR-Gaussian: Graph-Based Radiative Gaussian Splatting for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2508.02408/) (2025)
- [4DRGS: 4D Radiative Gaussian Splatting for Efficient 3D Vessel Reconstruction from Sparse-View Dynamic DSA Images](https://mlsanity.com/paper/2412.12919/) (2024)
- [NeAS: 3D Reconstruction from X-ray Images using Neural Attenuation Surface](https://mlsanity.com/paper/2503.07491/) (2025)
- [X-Field: A Physically Grounded Representation for 3D X-ray Reconstruction](https://mlsanity.com/paper/2503.08596/) (2025)
- [InnerGS: Internal Scenes Reconstruction and Segmentation via Factorized 3D Gaussian Splatting](https://mlsanity.com/paper/2508.13287/) (2025)
- [MedGS: Gaussian Splatting for Multi-Modal 3D Medical Imaging](https://mlsanity.com/paper/2509.16806/) (2025)
- [GEM: 3D Gaussian Splatting for Efficient and Accurate Cryo-EM Reconstruction](https://mlsanity.com/paper/2509.25075/) (2025)
- [DM4CT: Benchmarking Diffusion Models for Computed Tomography Reconstruction](https://mlsanity.com/paper/2602.18589/) (2026)
- [Time-resolved dynamic CBCT reconstruction using prior-model-free spatiotemporal Gaussian representation (PMF-STGR)](https://mlsanity.com/paper/2503.22139/) (2025)
- [NeRF-based CBCT Reconstruction needs Normalization and Initialization](https://mlsanity.com/paper/2506.19742/) (2025)
- [WIPES: Wavelet-based Visual Primitives](https://mlsanity.com/paper/2508.12615/) (2025)
- [Radioactive 3D Gaussian Ray Tracing for Tomographic Reconstruction](https://mlsanity.com/paper/2602.01057/) (2026)
- [Active View Selection with Perturbed Gaussian Ensemble for Tomographic Reconstruction](https://mlsanity.com/paper/2603.06852/) (2026)
- [MoRe-3DGSMR: Motion-resolved reconstruction framework for free-breathing pulmonary MRI based on 3D Gaussian representation](https://mlsanity.com/paper/2505.04959/) (2025)
- [Trans2-CBCT: A Dual-Transformer Framework for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2506.17425/) (2025)
- [DIGS: Dynamic CBCT Reconstruction using Deformation-Informed 4D Gaussian Splatting and a Low-Rank Free-Form Deformation Model](https://mlsanity.com/paper/2506.22280/) (2025)
- [NerT-CA: Efficient Dynamic Reconstruction from Sparse-view X-ray Coronary Angiography](https://mlsanity.com/paper/2507.19328/) (2025)
- [Zero-shot CT Super-Resolution using Diffusion-based 2D Projection Priors and Signed 3D Gaussians](https://mlsanity.com/paper/2508.15151/) (2025)
- [DenoiseGS: Gaussian Reconstruction Model for Burst Denoising](https://mlsanity.com/paper/2511.22939/) (2025)
- [GR-Diffusion: 3D Gaussian Representation Meets Diffusion in Whole-Body PET Reconstruction](https://mlsanity.com/paper/2602.11653/) (2026)
- [M-Gaussian: An Magnetic Gaussian Framework for Efficient Multi-Stack MRI Reconstruction](https://mlsanity.com/paper/2603.00145/) (2026)

## Abstract (arXiv)

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. Experiments on synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art approaches in accuracy and efficiency. Crucially, it delivers high-quality results in 4 minutes, which is 12× faster than NeRF-based methods and on par with traditional algorithms. Code and models are available on the project page https://github.com/Ruyi-Zha/r2gaussian.