  X-ray computed tomography (CT) is one of widely used diagnostic tools for
medical and dental tomographic imaging of the human body. However, the standard
filtered backprojection reconstruction method requires the complete knowledge
of the projection data. In the case of limited data, the inverse problem of CT
becomes more ill-posed, which makes the reconstructed image deteriorated by the
artifacts. In this paper, we consider two dimensional CT reconstruction using
the horizontally truncated projections. Over the decades, the numerous results
including the sparsity model based approach has enabled the reconstruction of
the image inside the region of interest (ROI) from the limited knowledge of the
data. However, unlike these existing methods, we try to reconstruct the entire
CT image from the limited knowledge of the sinogram via the tight frame
regularization and the simultaneous sinogram extrapolation. Our proposed model
shows more promising numerical simulation results compared with the existing
sparsity model based approach.
