Sinogram Upsampling via Sub-Riemannian Diffusion with Adaptive Weighting

Abstract

Computed tomography is a versatile imaging technique used to enable seeing internal structures of objects without opening or destroying them. This is possible through a process called tomographic reconstruction, which reconstructs images from projections of the object that are obtained by penetrating the object with beams of radiation, such as X-rays, from different angles. These projection data are often limited to low-resolution data in terms of projection angles. These limited or subsampled data make it difficult to obtain high-quality reconstruction results. Hence, upsampling projection data is necessary. In this paper, we propose a sinogram upsampling method via the sub-Riemannian diffusion process. We first lift the data into a feature space, and we fill in the missing angle parts by propagating information from the observed data to the missing parts. We observe that the sinogram with limited angle data has high directional dependency, and based on this observation, we suggest an adaptive weighting scheme to keep information propagating toward the missing regions. This adaptive weighting allows for diffusing toward the desired directions. The experimental results show the effectiveness of the proposed method in some scenarios regarding inpainting fine details, when compared to the existing model-based methods, such as Plug-and-Play and total generalized variation.