  We propose a new mass-mapping algorithm, specifically designed to recover
small-scale information from a combination of gravitational shear and flexion.
Including flexion allows us to supplement the shear on small scales in order to
increase the sensitivity to substructures and the overall resolution of the
convergence map without relying on strong lensing constraints. In order to
preserve all available small scale information, we avoid any binning of the
irregularly sampled input shear and flexion fields and treat the mass-mapping
problem as a general ill-posed inverse problem, regularised using a robust
multi-scale wavelet sparsity prior. The resulting algorithm incorporates
redshift, reduced shear, and reduced flexion measurements for individual
galaxies and is made highly efficient by the use of fast Fourier estimators. We
test our reconstruction method on a set of realistic weak lensing simulations
corresponding to typical HST/ACS cluster observations and demonstrate our
ability to recover substructures with the inclusion of flexion which are lost
if only shear information is used. In particular, we can detect substructures
at the 15$^{\prime \prime}$ scale well outside of the critical region of the
clusters. In addition, flexion also helps to constrain the shape of the central
regions of the main dark matter halos. Our mass-mapping software, called
Glimpse2D, is made freely available at
http://www.cosmostat.org/software/glimpse .

Cosmology and Nongalactic Astrophysics