Deep Learning for space-variant deconvolution in galaxy surveys

Starck 1 1 Laboratoire AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, F-91191 Gif-sur-Yvette, France 2 ONERA - The French Aerospace Lab, 6 chemin de la V auve aux Granges, BP 80100, FR-91123 P ALAISEAU cedex, France November 4, 2019 ABSTRACT Deconvolution of large survey images with millions of galaxies requires to develop a new generation of methods which can take into account a space variant Point Spread Function (PSF) and have to be at the same time accurate and fast. We investigate in this paper how Deep Learning (DL) could be used to perform this task. We employ a U-NET Deep Neural Network (DNN) architecture to learn in a supervised setting parameters adapted for galaxy image processing and study two strategies for deconvolution. The first approach is a post-processing of a mere Tikhonov deconvolution with closed form solution and the second one is an iterative deconvolution framework based on the Alternating Direction Method of Multipliers (ADMM). Our numerical results based on GREA T3 simulations with realistic galaxy images and PSFs show that our two approaches outperforms standard techniques based on convex optimization, whether assessed in galaxy image reconstruction or shape recovery. The approach based on Tikhonov deconvolution leads to the most accurate results except for ellipticity errors at high signal to noise ratio where the ADMM approach performs slightly better, is also more computation-time e fficient to process a large number of galaxies, and is therefore recommended in this scenario. Methods:statistical, Methods:data analysis, Methods:numerical 1. Introduction Deconvolution of large galaxy survey images requires to take into account spatial-variation of the Point Spread Function (PSF) across the field of view. The PSF field is usually estimated beforehand, via parametric models and simulations as in Krist et al. (2011) or directly estimated from the (noisy) observations of stars in the field of view (Bertin 2011; Kuijken et al. 2015; Zuntz et al. 2018; Mboula et al. 2016; Schmitz et al. 2019). Even with the "perfect" knowledge of the PSF, this ill-posed deconvolution problem is challenging, in particular due to the size of the image to process. Starck et al. (2000) proposed an Object-Oriented Deconvolution, consisting in first detecting galaxies and then deconvolving each object independently. Following this idea, Farrens et al. (2017) introduced a space-variant deconvolution approach for galaxy images, based on two regularization strategies: using either a sparse prior in a transformed domain (Starck et al. 2015a) or trying to learn unsupervisedly a low-dimensional subspace for galaxy representation using a low-rank prior on the recovered galaxy images.