The Very Knotty Lenser: exploring the role of regularization in source
  and potential reconstructions using Gaussian Process Regression
  Reconstructing lens potentials and lensed sources can easily become an
underconstrained problem, even when the degrees of freedom are low, due to
degeneracies, particularly when potential perturbations superimposed on a
smooth lens are included. Regularization has traditionally been used to
constrain the solutions where the data failed to do so, e.g. in unlensed parts
of the source. In this exploratory work, we go beyond the usual choices of
regularization and adopt observationally motivated priors for the source
brightness. We also perform a similar comparison when reconstructing lens
potential perturbations, which are assumed to be stationary, i.e. permeate the
entire field of view. We find that physically motivated priors lead to lower
residuals, avoid overfitting, and are decisively preferred within a Bayesian
quantitative framework in all the examples considered. For the perturbations,
choosing the wrong regularization can have a detrimental effect that even
high-quality data cannot correct for, while using a purely smooth lens model
can absorb them to a very high degree and lead to biased solutions. Finally,
our new implementation of the semi-linear inversion technique provides the
first quantitative framework for measuring degeneracies between the source and
the potential perturbations.
