aski: full-sky lensing map-making algorithms

• Published in: Monthly notices of the Royal Astronomical Society Vol. 401; no. 2; pp. 705 - 726
• Main Authors: Pichon, C., Thiébaut, E., Prunet, S., Benabed, K., Colombi, S., Sousbie, T., Teyssier, R.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.01.2010; Wiley-Blackwell; Oxford University Press; Oxford University Press (OUP): Policy P - Oxford Open Option A
• Subjects: Algorithms; Astronomy; Astrophysics; Earth, ocean, space; Exact sciences and technology; gravitational lensing; Gravity; Image processing systems; large-scale structure of Universe; methods: N-body simulations; methods: statistical; Sciences of the Universe; Simulation; Star maps; Stars & galaxies; surveys; techniques: image processing; methods: statistical; techniques: image processing; methods; large-scale structure of Universe; surveys; gravitational lensing; body simulations; Shear; Galaxies; Image processing; Gravitational lensing; N body system; Large-scale structure; Sky surveys; methods: N-body simulations; Power spectra; Statistical moment; Digital simulation; Signal-to-noise ratio; Topology; Statistical method; Point sources; Deconvolution; Algorithms; Quality factor; techniques; Nonlinearity; Models; Regularization; Astrophysics - Cosmology and Nongalactic Astrophysics
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2009.15609.x

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 SExtractor. 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 ℓ1−ℓ2 penalties are imposed during the iterative deconvolution. The quality of the convergence inversion is investigated on noisy maps derived from the horizon-4πN-body simulation with a signal-to-noise ratio (S/N) within the range ℓcut= 500–2500, with and without Galactic cuts, and quantified using one-point statistics (S3 and S4), 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 ℓ1−ℓ2 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.