FCDM: A Physics-Guided Bidirectional Frequency Aware Convolution and Diffusion-Based Model for Sinogram Inpainting

Computed tomography (CT) is widely used in scientific imaging systems such as synchrotron and laboratory-based nano-CT, but acquiring full-view sinograms requires high radiation dose and long scan times. Sparse-view CT reduces this burden but produces incomplete sinograms with structured signal loss, degrading reconstruction quality. Unlike RGB images, sinograms encode globally coupled projections and exhibit directional spectral patterns, making conventional RGB-oriented inpainting methods, including diffusion models, ineffective because they ignore angular dependencies and physical constraints inherent to tomographic data. We propose FCDM, a diffusion-based framework for sinogram restoration that incorporates bidirectional frequency reasoning, angular-aware masking, and physics-guided regularization to preserve global structure and physical plausibility. Experiments on real-world datasets show that FCDM consistently outperforms existing baselines, achieving over 0.93 SSIM and 31 dB PSNR across diverse sparse-view settings.