Path-length-aware sinogram completion via direct moment enforcement for metal artifact reduction in X-ray CT

High-density metallic objects often produce missing or severely corrupted projection data, resulting in strong streak artifacts in x-ray computed tomography (CT) images. In this paper, we propose a path-length-aware sinogram completion framework that combines interpolation in the mean attenuation domain with direct enforcement of low-order Helgason-Ludwig consistency conditions. The missing projections are first estimated using a Hermite-type interpolation that explicitly accounts for x-ray path length. Moment consistency is then restored through a probabilistic perturbation scheme based on compactly supported probability density functions, avoiding the need for solving a large-scale constrained optimization problem. Numerical experiments using both a simulated phantom and a dental CT model demonstrate that the proposed method generally achieves improved sinogram consistency and better image quality than linear interpolation-based metal artifact reduction (LI-MAR), normalized MAR (NMAR), and the TV-based iterative MAR method (TV-MAR), while preserving important anatomical structures. The proposed framework provides an efficient and physically motivated approach for MAR in x-ray CT.