  Computed tomography and magnetic resonance imaging are two widely used
clinical imaging modalities for non-invasive diagnosis. However, both of these
modalities come with certain problems. CT uses harmful ionising radiation, and
MRI suffers from slow acquisition speed. Both problems can be tackled by
undersampling, such as sparse sampling. However, such undersampled data leads
to lower resolution and introduces artefacts. Several techniques, including
deep learning based methods, have been proposed to reconstruct such data.
However, the undersampled reconstruction problem for these two modalities was
always considered as two different problems and tackled separately by different
research works. This paper proposes a unified solution for both sparse CT and
undersampled radial MRI reconstruction, achieved by applying Fourier
transform-based pre-processing on the radial MRI and then finally
reconstructing both modalities using sinogram upsampling combined with filtered
back-projection. The Primal-Dual network is a deep learning based method for
reconstructing sparsely-sampled CT data. This paper introduces Primal-Dual
UNet, which improves the Primal-Dual network in terms of accuracy and
reconstruction speed. The proposed method resulted in an average SSIM of
0.932\textpm0.021 while performing sparse CT reconstruction for fan-beam
geometry with a sparsity level of 16, achieving a statistically significant
improvement over the previous model, which resulted in 0.919\textpm0.016.
Furthermore, the proposed model resulted in 0.903\textpm0.019 and
0.957\textpm0.023 average SSIM while reconstructing undersampled brain and
abdominal MRI data with an acceleration factor of 16, respectively -
statistically significant improvements over the original model, which resulted
in 0.867\textpm0.025 and 0.949\textpm0.025.
