X2-Gaussian

4D Radiative Gaussian Splatting for Continuous-time Tomographic Reconstruction

Weihao Yu1, Yuanhao Cai2, Ruyi Zha3, Zhiwen Fan4, Chenxin Li1, Yixuan Yuan1
1The Chinese University of Hong Kong 2Johns Hopkins University 3The Australian National University 4University of Texas at Austin
Paper Code
First demonstration GIF
Second demonstration GIF
Third demonstration GIF
Overview of X²-Gaussian

X$^2$-Gaussian demonstrates state-of-the-art reconstruction performance.

Overview of X²-Gaussian

X$^2$-Gaussian achieves genuine continuous-time CT reconstruction without phase-binning. The figure illustrates temporal variations of lung volume in 4D CT reconstructed by X$^2$-Gaussian.

Abstract

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 X$^2$-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, X$^2$-Gaussian advances high-fidelity 4D CT reconstruction for dynamic clinical imaging.

Approach

Pipeline Image

We design dynamic Gaussian motion modeling for continuous-time reconstruction, and self-supervised respiratory motion learning for estimating breathing cycle autonomously.

Results

Pipeline Image

BibTeX

@article{yu2025x,
    title={X $\^{}$\{$2$\}$ $-Gaussian: 4D Radiative Gaussian Splatting for Continuous-time Tomographic Reconstruction},
    author={Yu, Weihao and Cai, Yuanhao and Zha, Ruyi and Fan, Zhiwen and Li, Chenxin and Yuan, Yixuan},
    journal={arXiv preprint arXiv:2503.21779},
    year={2025}
  }