  X-ray Computed Tomography (CT) is one of the most important diagnostic
imaging techniques in clinical applications. Sparse-view CT imaging reduces the
number of projection views to a lower radiation dose and alleviates the
potential risk of radiation exposure. Most existing deep learning (DL) and deep
unfolding sparse-view CT reconstruction methods: 1) do not fully use the
projection data; 2) do not always link their architecture designs to a
mathematical theory; 3) do not flexibly deal with multi-sparse-view
reconstruction assignments. This paper aims to use mathematical ideas and
design optimal DL imaging algorithms for sparse-view tomography
reconstructions. We propose a novel dual-domain deep unfolding unified
framework that offers a great deal of flexibility for multi-sparse-view CT
reconstruction with different sampling views through a single model. This
framework combines the theoretical advantages of model-based methods with the
superior reconstruction performance of DL-based methods, resulting in the
expected generalizability of DL. We propose a refinement module that utilizes
unfolding projection domain to refine full-sparse-view projection errors, as
well as an image domain correction module that distills multi-scale geometric
error corrections to reconstruct sparse-view CT. This provides us with a new
way to explore the potential of projection information and a new perspective on
designing network architectures. All parameters of our proposed framework are
learnable end to end, and our method possesses the potential to be applied to
plug-and-play reconstruction. Extensive experiments demonstrate that our
framework is superior to other existing state-of-the-art methods. Our source
codes are available at https://github.com/fanxiaohong/MVMS-RCN.
