Deep learning for a space-variant deconvolution in galaxy surveys

F Sureau,J.-L Starck,A Lechat

doi:10.1051/0004-6361/201937039

Abstract

The deconvolution of large survey images with millions of galaxies requires developing a new generation of methods that can take a space-variant point spread function into account. These methods have also to be accurate and fast. We investigate how deep learning might be used to perform this task. We employed a U-net deep neural network architecture to learn parameters that were adapted for galaxy image processing in a supervised setting and studied two deconvolution strategies. The first approach is a post-processing of a mere Tikhonov deconvolution with closed-form solution, and the second approach is an iterative deconvolution framework based on the alternating direction method of multipliers (ADMM). Our numerical results based on GREAT3 simulations with realistic galaxy images and point spread functions show that our two approaches outperform standard techniques that are based on convex optimization, whether assessed in galaxy image reconstruction or shape recovery. The approach based on a Tikhonov deconvolution leads to the most accurate results, except for ellipticity errors at high signal-to-noise ratio. The ADMM approach performs slightly better in this case. Considering that the Tikhonov approach is also more computation-time efficient in processing a large number of galaxies, we recommend this approach in this scenario.

Highlights

The deconvolution of large galaxy survey images requires that the spatial variation of the point spread function (PSF) across the field of view is taken into account
The proposed deep-learning approaches perform in median pixel and ellipticity errors, and they outperform the sparse and low-rank approaches: the median pixel error is reduced by almost 14% (9%) for the Tikhonet (ADMMnet) approach compared to sparse recovery, and the ellipticity errors are reduced by about 13% for both approaches
We have proposed two new space-variant deconvolution strategies for galaxy images based on deep neural networks while keeping all knowledge of the PSF in the forward model: the Tikhonet approach is a post-processing approach of a simple Tikhonov deconvolution with a DNN, and the ADMMnet approach is based on regularization by a DNN denoiser inside an iterative alternating direction method of multipliers (ADMM) PnP algorithm for deconvolution

Summary

Introduction

The deconvolution of large galaxy survey images requires that the spatial variation of the point spread function (PSF) across the field of view is taken into account. Starck et al (2000) proposed an object-oriented deconvolution that consists of first detecting galaxies and deconvolving each object independently, taking the PSF at the position of the center of the galaxy into account (but not the variation in the PSF field at the galaxy scale) Following this idea, Farrens et al (2017) introduced a space-variant deconvolution approach for galaxy images that is based on two regularization strategies: using either a sparse prior in a transformed domain (Starck et al 2015a), or trying to learn without supervision a low-dimensional subspace for galaxy representation using a low-rank prior on the recovered galaxy images. When a sufficient number of galaxies were processed jointly (more than 1000), the authors found that the low-rank approach provided significantly lower ellipticity errors than sparsity This illustrates the importance of learning adequate representations for galaxies.

Methods

Results

Conclusion