# X2-Gaussian: 4D Radiative Gaussian Splatting for Continuous-time Tomographic Reconstruction

arXiv: https://arxiv.org/abs/2503.21779 · HTML: https://mlsanity.com/paper/2503.21779/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 73 references that are in the map.
- First posted on arXiv 27 Mar 2025.

## Builds on (most cited first, 27 of 27)

- [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)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Gaussian Splatting SLAM](https://mlsanity.com/paper/2312.06741/) (2023)
- [Fast Dynamic Radiance Fields with Time-Aware Neural Voxels](https://mlsanity.com/paper/2205.15285/) (2022)
- [GRM: Large Gaussian Reconstruction Model for Efficient 3D Reconstruction and Generation](https://mlsanity.com/paper/2403.14621/) (2024)
- [GS-SLAM: Dense Visual SLAM with 3D Gaussian Splatting](https://mlsanity.com/paper/2311.11700/) (2023)
- [DreamGaussian4D: Generative 4D Gaussian Splatting](https://mlsanity.com/paper/2312.17142/) (2023)
- [Gaussian-SLAM: Photo-realistic Dense SLAM with Gaussian Splatting](https://mlsanity.com/paper/2312.10070/) (2023)
- [Gaussian in the Wild: 3D Gaussian Splatting for Unconstrained Image Collections](https://mlsanity.com/paper/2403.15704/) (2024)
- [NAF: Neural Attenuation Fields for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2209.14540/) (2022)
- [Structure-Aware Sparse-View X-ray 3D Reconstruction](https://mlsanity.com/paper/2311.10959/) (2023)
- [R2-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction](https://mlsanity.com/paper/2405.20693/) (2024)
- [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)
- [Sparse-view Cone Beam CT Reconstruction using Data-consistent Supervised and Adversarial Learning from Scarce Training Data](https://mlsanity.com/paper/2201.09318/) (2022)
- [BREAK: Bronchi Reconstruction by gEodesic transformation And sKeleton embedding](https://mlsanity.com/paper/2202.00002/) (2022)
- [Spatiotemporal Gaussian Optimization for 4D Cone Beam CT Reconstruction from Sparse Projections](https://mlsanity.com/paper/2501.04140/) (2025)
- [GeoT: Geometry-guided Instance-dependent Transition Matrix for Semi-supervised Tooth Point Cloud Segmentation](https://mlsanity.com/paper/2503.16976/) (2025)

## Built on by (most cited first, 6 of 6)

- [GEM: 3D Gaussian Splatting for Efficient and Accurate Cryo-EM Reconstruction](https://mlsanity.com/paper/2509.25075/) (2025)
- [Active View Selection with Perturbed Gaussian Ensemble for Tomographic Reconstruction](https://mlsanity.com/paper/2603.06852/) (2026)
- [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)
- [3D Gaussian Splatting for Annular Dark Field Scanning Transmission Electron Microscopy Tomography Reconstruction](https://mlsanity.com/paper/2604.04693/) (2026)
- [TG-Field: Geometry-Aware Radiative Gaussian Fields for Tomographic Reconstruction](https://mlsanity.com/paper/2602.11705/) (2026)

## Abstract (arXiv)

Four-dimensional computed tomography (4D CT) reconstruction is crucial for capturing dynamic anatomical changes but faces inherent limitations from conventional phase-binning workflows. Current methods discretize temporal resolution into fixed phases with respiratory gating devices, introducing motion misalignment and restricting clinical practicality. In this paper, We propose X2-Gaussian, a novel framework that enables continuous-time 4D-CT reconstruction by integrating dynamic radiative Gaussian splatting with self-supervised respiratory motion learning. Our approach models anatomical dynamics through a spatiotemporal encoder-decoder architecture that predicts time-varying Gaussian deformations, eliminating phase discretization. To remove dependency on external gating devices, we introduce a physiology-driven periodic consistency loss that learns patient-specific breathing cycles directly from projections via differentiable optimization. Extensive experiments demonstrate state-of-the-art performance, achieving a 9.93 dB PSNR gain over traditional methods and 2.25 dB improvement against prior Gaussian splatting techniques. By unifying continuous motion modeling with hardware-free period learning, X2-Gaussian advances high-fidelity 4D CT reconstruction for dynamic clinical imaging. Code is publicly available at: https://x2-gaussian.github.io/.