GR-Gaussian: Graph-Based Radiative Gaussian Splatting for Sparse-View Tomographic Reconstruction

Abstract

Computed tomography (CT) reconstruction under sparse-view acquisition is fundamentally ill-posed. Recently, 3D Gaussian Splatting (3DGS) has emerged as an efficient alternative to implicit neural fields for per-case tomographic reconstruction, offering explicit geometric primitives and fast differentiable rendering. However, under sparse projection supervision, existing 3DGS-based CT methods can become unstable because the Gaussian primitives are optimized largely independently, often leading to overfitting and needle-like artifacts. In this work, we propose GR-Gaussian, a graph-regularized radiative 3DGS framework for sparse-view CT reconstruction. Rather than introducing a new volumetric representation, our method augments radiative Gaussian optimization with local graph-guided structural cues. Specifically, we introduce two components: (1) a denoised point-cloud initialization strategy (De-Init), which filters artifact-contaminated FDK priors to provide a more reliable initialization for Gaussian placement and neighborhood construction; and (2) a Pixel-Graph-Aware (PGA) densification criterion, which supplements the baseline pixel-aware densification signal with local density contrast measured on the Gaussian neighborhood graph. In addition, we incorporate graph Laplacian and volumetric total variation regularization to improve structural consistency during optimization. Experiments on the X-3D and real-world CT datasets show that GR-Gaussian consistently improves reconstruction quality over the evaluated baselines, while providing cleaner structures and stronger suppression of sparse-view artifacts. These results indicate that initialization and graph-guided densification are effective practical extensions to radiative 3DGS for sparse-view CT reconstruction.