  Machine learning techniques have been successfully applied to
super-resolution tasks on natural images where visually pleasing results are
sufficient. However in many scientific domains this is not adequate and
estimations of errors and uncertainties are crucial. To address this issue we
propose a Bayesian framework that decomposes uncertainties into epistemic and
aleatoric uncertainties. We test the validity of our approach by
super-resolving images of the Sun's magnetic field and by generating maps
measuring the range of possible high resolution explanations compatible with a
given low resolution magnetogram.
