  Compared to standard tomographic reconstruction, iterative approaches offer
the possibility to account for extraneous experimental influences, which allows
for a suppression of related artifacts. However, the inclusion of corresponding
parameters in the iterative forward model typically leads to longer computation
times. Here, we demonstrate experimentally for phase sensitive X-ray imaging
based on the edge illumination principle that inadequately sampled illumination
curves result in ring artifacts in tomographic reconstructions. We take
advantage of appropriately sampled illumination curves instead, which enables
us to eliminate the corresponding parameter from the forward model and
substantially increase computational speed. In addition, we demonstrate a 30\%
improvement in spatial resolution of the iterative approach compared with the
standard non-iterative single shot approach. Further, we report on several
significant improvements in our numerical implementation of the iterative
approach, which we make available online with this publication. Finally, we
show that the combination of both experimental and algorithmic advancement lead
to a total speed increase by one order of magnitude and an improved contrast to
noise ratio in the reconstructions.
