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We propose a new mass-mapping algorithm, specifically designed to recoversmall-scale information from a combination of gravitational shear and flexion.Including flexion allows us to supplement the shear on small scales in order toincrease the sensitivity to substructures and the overall resolution of theconvergence map without relying on strong lensing constraints. In order topreserve all available small scale information, we avoid any binning of theirregularly sampled input shear and flexion fields and treat the mass-mappingproblem as a general ill-posed inverse problem, regularised using a robustmulti-scale wavelet sparsity prior. The resulting algorithm incorporatesredshift, reduced shear, and reduced flexion measurements for individualgalaxies and is made highly efficient by the use of fast Fourier estimators. Wetest our reconstruction method on a set of realistic weak lensing simulationscorresponding to typical HST/ACS cluster observations and demonstrate ourability to recover substructures with the inclusion of flexion which are lostif only shear information is used. In particular, we can detect substructuresat the 15$^{\prime \prime}$ scale well outside of the critical region of theclusters. In addition, flexion also helps to constrain the shape of the centralregions of the main dark matter halos. Our mass-mapping software, calledGlimpse2D, is made freely available athttp://www.cosmostat.org/software/glimpse .

High Resolution Weak Lensing Mass-Mapping Combining Shear and Flexion