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ABSTRACT  Within the context of upcoming full‐sky lensing surveys, the edge‐preserving non‐linear algorithm  aski  ( All‐Sky κ Inversion ) is presented. Using the framework of Maximum A Posteriori inversion, it aims at recovering the  optimal  full‐sky convergence map from noisy surveys with masks.  aski  contributes two steps: (i) CCD images of possibly crowded galactic fields are deblurred using  automated  edge‐preserving deconvolution; (ii) once the reduced shear is estimated using standard techniques, the partially masked convergence map is also inverted via an edge‐preserving method.  The efficiency of the deblurring of the image is quantified by the relative gain in the quality factor of the reduced shear, as estimated by SE xtractor . Cross‐validation as a function of the number of stars removed yields an automatic estimate of the optimal level of regularization for the deconvolution of the galaxies. It is found that when the observed field is crowded, this gain can be quite significant for realistic ground‐based 8‐m class surveys. The most significant improvement occurs when both positivity and edge‐preserving  ℓ 1 −ℓ 2   penalties are imposed during the iterative deconvolution.  The quality of the convergence inversion is investigated on noisy maps derived from the  horizon ‐4π N ‐body simulation with a signal‐to‐noise ratio (S/N) within the range  ℓ cut = 500–2500 , with and without Galactic cuts, and quantified using one‐point statistics ( S  3  and  S  4 ), power spectra, cluster counts, peak patches and the skeleton. It is found that (i) the reconstruction is able to interpolate and extrapolate within the Galactic cuts/non‐uniform noise; (ii) its sharpness‐preserving penalization avoids strong biasing near the clusters of the map; (iii) it reconstructs well the shape of the PDF as traced by its skewness and kurtosis; (iv) the geometry and topology of the reconstructed map are close to the initial map as traced by the peak patch distribution and the skeleton's differential length; (v) the two‐point statistics of the recovered map are consistent with the corresponding smoothed version of the initial map; (vi) the distribution of point sources is also consistent with the corresponding smoothing, with a significant improvement when  ℓ 1 −ℓ 2   prior is applied. The contamination of B modes when realistic Galactic cuts are present is also investigated. Leakage mainly occurs on large scales. The non‐linearities implemented in the model are significant on small scales near the peaks in the field.

aski : full‐sky lensing map‐making algorithms