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. Project website at: https://x2-gaussian.github.io/.

翻译：四维计算机断层扫描（4D CT）重建对于捕捉动态解剖结构变化至关重要，但传统相位分选工作流程存在固有局限性。现有方法通过呼吸门控设备将时间分辨率离散化为固定相位，导致运动失准并限制了临床实用性。本文提出X$^2$-高斯，一种通过将动态辐射高斯溅射与自监督呼吸运动学习相结合来实现连续时间4D-CT重建的新型框架。我们的方法通过时空编码器-解码器架构预测时变高斯形变来建模解剖结构动态，从而消除相位离散化。为摆脱对外部门控设备的依赖，我们引入生理驱动的周期性一致性损失函数，通过可微分优化直接从投影数据中学习患者特异性呼吸周期。大量实验证明了最先进的性能，相较于传统方法获得9.93 dB的PSNR提升，相对先前高斯溅射技术亦有2.25 dB的改进。通过将连续运动建模与无硬件周期学习相统一，X$^2$-高斯推动了动态临床成像领域的高保真4D CT重建。项目网站位于：https://x2-gaussian.github.io/。