The analysis of weak lensing data requires to account for missing data such as masking out of bright stars. To date, the majority of lensing analyses uses the two point-statistics of the cosmic shear field. These can either be studied directly using the two-point correlation function, or in Fourier space, using the power spectrum. The two-point correlation function is unbiased by missing data but its direct calculation will soon become a burden with the exponential growth of astronomical data sets. The power spectrum is fast to estimate but a mask correction should be estimated. Other statistics can be used but these are strongly sensitive to missing data. The solution that is proposed by FASTLens is to properly fill-in the gaps with only NlogN operations, leading to a complete weak lensing mass map from which one can compute straight forwardly and with a very good accuracy any kind of statistics like power spectrum or bispectrum.

Glimpse, also known as Glimpse2D, is a weak lensing mass-mapping tool that relies on a robust sparsity-based regularization scheme to recover high resolution convergence from either gravitational shear alone or from a combination of shear and flexion. Including flexion allows the supplementation of the shear on small scales in order to increase the sensitivity to substructures and the overall resolution of the convergence map. To preserve all available small scale information, Glimpse avoids any binning of the irregularly sampled input shear and flexion fields and treats the mass-mapping problem as a general ill-posed inverse problem, regularized using a 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.