  We present a strong lensing modeling technique based on versatile basis sets
for the lens and source planes. Our method uses high performance Monte Carlo
algorithms, allows for an adaptive build up of complexity and bridges the gap
between parametric and pixel based reconstruction methods. We apply our method
to a HST image of the strong lens system RXJ1131-1231 and show that our method
finds a reliable solution and is able to detect substructure in the lens and
source planes simultaneously. Using mock data we show that our method is
sensitive to sub-clumps with masses four orders of magnitude smaller than the
main lens, which corresponds to about $10^8 M_{\odot}$, without prior knowledge
on the position and mass of the sub-clump. The modelling approach is flexible
and maximises automation to facilitate the analysis of the large number of
strong lensing systems expected in upcoming wide field surveys. The resulting
search for dark sub-clumps in these systems, without mass-to-light priors,
offers promise for probing physics beyond the standard model in the dark matter
sector.
