Splatting Without Discrete Density Control: Lifted Gaussian-Mixture Kernel for CT Reconstruction

3D Gaussian Splatting (3DGS) has become one of the key paradigms in 3D reconstruction, offering an efficient explicit representation method with real-time rendering capabilities. It has demonstrated significant potential in X-ray computed tomography (CT) reconstruction, but existing methods rely on a discrete Adaptive Density Control (ADC) mechanism based on hard-threshold cloning, splitting, and pruning decisions. The threshold parameters are coupled with hyperparameters such as the objective function design, leading to potential imbalances in the Gaussian distribution under different reconstruction conditions—particularly in ill-posed reconstruction—which require multiple manual adjustments and thus severely limit the performance ceiling of the reconstruction method. This paper utilizes a dimension-elevated Gaussian mixed-kernel affine transformation to convert the splitting and merging behaviors of Gaussian kernels into continuously differentiable motion trajectories, enabling their integration into the 3D reconstruction optimization chain without reliance on hyperparameter thresholds. Based on this mechanism, we have constructed a CT 3D reconstruction framework that allows users to allocate a budget for the number of Gaussian kernels to be reconstructed. Experiments show that, with the same number of kernels, our method outperforms the ADC-based 3DGS reconstruction method. Furthermore, when considering larger kernel budgets, ADC begins to show signs of fatigue or even a decline in performance without the use of any additional Gaussian kernel scheduling or pruning strategies, whereas our method maintains superior performance and continues to improve as the kernel budget increases.