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Reconstructing lens potentials and lensed sources can easily become anunderconstrained problem, even when the degrees of freedom are low, due todegeneracies, particularly when potential perturbations superimposed on asmooth lens are included. Regularization has traditionally been used toconstrain the solutions where the data failed to do so, e.g. in unlensed partsof the source. In this exploratory work, we go beyond the usual choices ofregularization and adopt observationally motivated priors for the sourcebrightness. We also perform a similar comparison when reconstructing lenspotential perturbations, which are assumed to be stationary, i.e. permeate theentire field of view. We find that physically motivated priors lead to lowerresiduals, avoid overfitting, and are decisively preferred within a Bayesianquantitative framework in all the examples considered. For the perturbations,choosing the wrong regularization can have a detrimental effect that evenhigh-quality data cannot correct for, while using a purely smooth lens modelcan absorb them to a very high degree and lead to biased solutions. Finally,our new implementation of the semi-linear inversion technique provides thefirst quantitative framework for measuring degeneracies between the source andthe potential perturbations.

The Very Knotty Lenser: exploring the role of regularization in source and potential reconstructions using Gaussian Process Regression