  The sparse-views x-ray computed tomography (CT) is essential for medical
diagnosis and industrial nondestructive testing. However, in particular, the
reconstructed image usually suffers from complex artifacts and noise, when the
sampling is insufficient. In order to deal such issue, a full-automatic
reconstruction (FAR) net is proposed for sparse-views CT reconstruction via
deep learning technique. Different with the usual network in deep learning
reconstruction, the proposed neural network is an End-to-End network by which
the image is predicted directly from projection data. The main challenge for
such a FAR net is the space complexity of the CT reconstruction in
full-connected (FC) network. For a CT image with the size $N \times N$ , a
typical requirement of memory space for the image reconstruction is $O(N^{4})$,
for which is unacceptable by conventional calculation device, e.g. GPU
workstation. In this paper, we utilize a series of smaller FC layers to replace
the huge based on the sparse nonnegative matrix factorization (SNMF) theory. By
applying such an approach, the FAR net is able to reconstruct sparse-views CT
images with the size $512\times 512$ on only one workstation. Furthermore, a
Res-Unet structure is composed in the FAR net for suppressing the artifacts and
noise caused by under-sampling data. The results of numerical experiments show
that the projection matrix and the FAR net is able to reconstruct the CT image
from sparse-views projection data with a superior quality than conventional
method such as FBP and optimization based approach. Meanwhile, the
factorization for the inverse projection matrix is validated in numerical.
