  Modeling the mass distribution of galaxy-scale strong gravitational lenses is
a task of increasing difficulty. The high-resolution and depth of imaging data
now available render simple analytical forms ineffective at capturing lens
structures spanning a large range in spatial scale, mass scale, and morphology.
In this work, we address the problem with a novel multiscale method based on
wavelets. We tested our method on simulated Hubble Space Telescope (HST)
imaging data of strong lenses containing the following different types of mass
substructures making them deviate from smooth models: (1) a localized small
dark matter subhalo, (2) a Gaussian random field (GRF) that mimics a
nonlocalized population of subhalos along the line of sight, and (3)
galaxy-scale multipoles that break elliptical symmetry. We show that wavelets
are able to recover all of these structures accurately. This is made
technically possible by using gradient-informed optimization based on automatic
differentiation over thousands of parameters, which also allow us to sample the
posterior distributions of all model parameters simultaneously. By
construction, our method merges the two main modeling paradigms - analytical
and pixelated - with machine-learning optimization techniques into a single
modular framework. It is also well-suited for the fast modeling of large
samples of lenses. All methods presented here are publicly available in our new
Herculens package.
