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

Abstract: Computed tomography (CT) is widely used in industrial and medical imaging, but sparse-view scanning reduces radiation exposure at the cost of incomplete sinograms and challenging reconstruction. Existing RGB-based inpainting models struggle with severe feature entanglement, while sinogram-specific methods often lack explicit physics constraints. We propose FCDM, a physics-guided, frequency-aware sinogram inpainting framework. It integrates bidirectional frequency-domain convolutions to disentangle overlapping features while enforcing total absorption and frequency-domain consistency via a physics-informed loss. To enhance diffusion-based restoration, we introduce a Fourier-enhanced mask embedding to encode angular dependencies and a frequency-adaptive noise scheduling strategy that incorporates a soft row-wise absorption constraint to maintain physical realism. Experiments on synthetic and real-world datasets show that FCDM outperforms existing methods, achieving SSIM over 0.95 and PSNR above 30 dB, with up to 33% and 29% improvements over baselines.