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

Computed tomography (CT) is widely used in scientific and medical imaging, but acquiring full-view sinograms requires high radiation dose and long scan times. Sparse-view CT alleviates this burden but yields incomplete sinograms with structured signal loss, hampering accurate reconstruction. Unlike RGB images, sinograms encode overlapping features along projection paths and exhibit directional spectral patterns. Standard inpainting models overlook these properties, treating missing data as local holes and neglecting angular dependencies and physical consistency. We propose~\modelname, a diffusion-based framework tailored for sinograms, which restores global structure through bidirectional frequency reasoning and angular-aware masking, while enforcing physical plausibility via physics-guided constraints and frequency-adaptive noise control. Experiments on synthetic and real-world datasets show that~\modelname~consistently outperforms baselines, achieving SSIM over 0.93 and PSNR above 31 dB across diverse sparse-view scenarios.