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. Project website at:this https URL.
View on arXiv@article{yu2025_2503.21779,
title={ X$^{2}$-Gaussian: 4D Radiative Gaussian Splatting for Continuous-time Tomographic Reconstruction },
author={ Weihao Yu and Yuanhao Cai and Ruyi Zha and Zhiwen Fan and Chenxin Li and Yixuan Yuan },
journal={arXiv preprint arXiv:2503.21779},
year={ 2025 }
}