  Increasingly in medical imaging has emerged an issue surrounding the
reconstruction of noisy images from raw measurement data. Where the forward
problem is the generation of raw measurement data from a ground truth image,
the inverse problem is the reconstruction of those images from the measurement
data. In most cases with medical imaging, classical inverse Radon transforms,
such as an inverse Fourier transform for MRI, work well for recovering clean
images from the measured data. Unfortunately in the case of X-Ray CT, where
undersampled data is very common, more than this is needed to resolve faithful
and usable images. In this paper, we explore the history of classical methods
for solving the inverse problem for X-Ray CT, followed by an analysis of the
state of the art methods that utilize supervised deep learning. Finally, we
will provide some possible avenues for research in the future.
