  X-ray computed tomographic infrastructures are medical imaging modalities
that rely on the acquisition of rays crossing examined objects while measuring
their intensity decrease. Physical measurements are post-processed by
mathematical reconstruction algorithms that may offer weaker or top-notch
consistency guarantees on the computed volumetric field. Superior results are
provided on the account of an abundance of low-noise measurements being
supplied. Nonetheless, such a scanning process would expose the examined body
to an undesirably large-intensity and long-lasting ionising radiation, imposing
severe health risks. One main objective of the ongoing research is the
reduction of the number of projections while keeping the quality performance
stable. Due to the under-sampling, the noise occurring inherently because of
photon-electron interactions is now supplemented by reconstruction artifacts.
Recently, deep learning methods, especially fully convolutional networks have
been extensively investigated and proven to be efficient in filtering such
deviations. In this report algorithms are presented that take as input a slice
of a low-quality reconstruction of the volume in question and aim to map it to
the reconstruction that is considered ideal, the ground truth. Above that, the
first system comprises two additional elements: firstly, it ensures the
consistency with the measured sinogram, secondly it adheres to constraints
proposed in classical compressive sampling theory. The second one, inspired by
classical ways of solving the inverse problem of reconstruction, takes an
iterative approach to regularise the hypothesis in the direction of the correct
result.
