Statistical and systematic uncertainties in pixel-based source
  reconstruction algorithms for gravitational lensing
  Gravitational lens modeling of spatially resolved sources is a challenging
inverse problem with many observational constraints and model parameters. We
examine established pixel-based source reconstruction algorithms for de-lensing
the source and constraining lens model parameters. Using test data for four
canonical lens configurations, we explore statistical and systematic
uncertainties associated with gridding, source regularisation, interpolation
errors, noise, and telescope pointing. Specifically, we compare two gridding
schemes in the source plane: a fully adaptive grid that follows the lens
mapping but is irregular, and an adaptive Cartesian grid. We also consider
regularisation schemes that minimise derivatives of the source (using two
finite difference methods) and introduce a scheme that minimises deviations
from an analytic source profile. Careful choice of gridding and regularisation
can reduce "discreteness noise" in the $\chi^2$ surface that is inherent in the
pixel-based methodology. With a gridded source, some degree of interpolation is
unavoidable, and errors due to interpolation need to be taken into account
(especially for high signal-to-noise data). Different realisations of the noise
and telescope pointing lead to slightly different values for lens model
parameters, and the scatter between different "observations" can be comparable
to or larger than the model uncertainties themselves. The same effects create
scatter in the lensing magnification at the level of a few percent for a peak
signal-to-noise ratio of 10, which decreases as the data quality improves.
