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X$^{2}$-Gaussian: 4D Radiative Gaussian Splatting for Continuous-time Tomographic Reconstruction

Weihao Yu, Yuanhao Cai, Ruyi Zha, Zhiwen Fan, Chenxin Li, Yixuan Yuan

TL;DR

This work proposes 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 and introduces a physiology-driven periodic consistency loss that learns patient-specific breathing cycles directly from projections via differentiable optimization.

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. Code is publicly available at: https://x2-gaussian.github.io/.

X$^{2}$-Gaussian: 4D Radiative Gaussian Splatting for Continuous-time Tomographic Reconstruction

TL;DR

This work proposes 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 and introduces a physiology-driven periodic consistency loss that learns patient-specific breathing cycles directly from projections via differentiable optimization.

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-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-Gaussian advances high-fidelity 4D CT reconstruction for dynamic clinical imaging. Code is publicly available at: https://x2-gaussian.github.io/.

Paper Structure

This paper contains 33 sections, 12 equations, 6 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. CT Reconstruction
  4. Gaussian Splatting
  5. Preliminaries
  6. Methods
  7. Overview
  8. Dynamic Gaussian Motion Modeling
  9. Decomposed Spatio-Temporal Encoding.
  10. Deformation-Aware Gaussian Decoding.
  11. Self-Supervised Respiratory Motion Learning
  12. Physiology-Driven Periodic Consistency Loss.
  13. Differentiable Cycle-Length Optimization.
  14. Optimization
  15. Loss Function.
  16. ...and 18 more sections

Figures (6)

  • Figure 1: Dynamic reconstruction results of the proposed X$^2$-Gaussian on public DIR Dataset castillo2009framework. The red dashed line is the reference line for diaphragm movement, and blue dashed box shows some tissue deformation. Our method demonstrates superior capability in continuous-time reconstruction, significantly outperforming existing approaches.
  • Figure 2: Framework of our X$^2$-Gaussian, which consists of two innovative components: (1) Dynamic Gaussian motion modeling for continuous-time reconstruction; (2) Self-Supervised respiratory motion learning for estimating breathing cycle autonomously.
  • Figure 3: Periodic display of respiratory motion ($T=3s$). A specific anatomical structure (framed by boxes of the same color) at time $t$ has the same position at time $t+nT$.
  • Figure 4: Convergence behavior of the learnable period $\hat{T}$. Without Bounded Cycle Shifts, $\hat{T}$ undergoes wide-ranging oscillations approaching half the true period. Without Log-Space Parameterization, the optimization curve exhibits large oscillations. With both techniques implemented, $\hat{T}$ converges stably and accurately to the correct breathing cycle.
  • Figure 5: Qualitative comparison of reconstruction results across coronal, sagittal, and axial planes. Our method shows superior performance in modeling dynamic regions (e.g. diaphragmatic motion and airway deformation) while preserving finer anatomical details compared to existing approaches.
  • ...and 1 more figures