  In this paper, we propose a sinogram inpainting network (SIN) to solve
limited-angle CT reconstruction problem, which is a very challenging ill-posed
issue and of great interest for several clinical applications. A common
approach to the problem is an iterative reconstruction algorithm with
regularization term, which can suppress artifacts and improve image quality,
but requires high computational cost.
  The starting point of this paper is the proof of inpainting function for
limited-angle sinogram is continuous, which can be approached by neural
networks in a data-driven method, granted by the universal approximation
theorem. Based on this, we propose SIN as the fitting function -- a
convolutional neural network trained to generate missing sinogram data
conditioned on scanned data. Besides CNN module, we design two differentiable
and rapid modules, Radon and Inverse Radon Transformer network, to encapsulate
the physical model in the training procedure. They enable new joint loss
functions to optimize both sinogram and reconstructed image in sync, which
improved the image quality significantly. To tackle the labeled data bottleneck
in clinical research, we form a sinogram-image-sinogram closed loop, and the
difference between sinograms can be used as training loss. In this way, the
proposed network can be self-trained, with only limited-angle data for
unsupervised domain adaptation.
  We demonstrate the performance of our proposed network on parallel beam X-ray
CT in lung CT datasets from Data Science Bowl 2017 and the ability of
unsupervised transfer learning in Zubal's phantom. The proposed method performs
better than state-of-art method SART-TV in PSNR and SSIM metrics, with
noticeable visual improvements in reconstructions.
