Adaptive Semi-linear Inversion of Strong Gravitational Lens Imaging
  We present a new pixelized method for the inversion of gravitationally lensed
extended source images which we term adaptive semi-linear inversion (SLI). At
the heart of the method is an h-means clustering algorithm which is used to
derive a source plane pixelization that adapts to the lens model magnification.
The distinguishing feature of adaptive SLI is that every pixelization is
derived from a random initialization, ensuring that data discretization is
performed in a completely different and unique way for every lens model
parameter set. We compare standard SLI on a fixed source pixel grid with the
new method and demonstrate the shortcomings of the former when modeling
singular power law ellipsoid (SPLE) lens profiles. In particular, we
demonstrate the superior reliability and efficiency of adaptive SLI which, by
design, fixes the number of degrees of freedom (NDOF) of the optimization and
thereby removes biases present with other methods that allow the NDOF to vary.
In addition, we highlight the importance of data discretization in pixel-based
inversion methods, showing that adaptive SLI averages over significant
systematics that are present when a fixed source pixel grid is used. In the
case of the SPLE lens profile, we show how the method successfully samples its
highly degenerate posterior probability distribution function with a single
non-linear search. The robustness of adaptive SLI provides a firm foundation
for the development of a strong lens modeling pipeline, which will become
necessary in the short-term future to cope with the increasing rate of
discovery of new strong lens systems.
