Removing the aberrations introduced by the Point Spread Function (PSF) is a fundamental aspect of astronomical image processing. The presence of noise in observed images makes deconvolution a nontrivial task that necessitates the use of regularisation. This task is particularly difficult when the PSF varies spatially as is the case for big surveys such as LSST or Euclid surveys. It becomes a fantastic challenge when the PSF field is unknown. The first step is therefore to estimate accurately the PSF field. In practice, isolated stars provide a measurement of the PSF at a given location in the telescope field of view. Thus we propose an algorithm to recover the PSF field, using the measurements available at few these locations. This amounts to solving an inverse problem that we regularize using both matrix factorization and a sparsity. Then we show that, for these new surveys providing images containing thousand of galaxies, the deconvolution regularisation problem can be considered from a completely new perspective. In fact, one can assume that galaxies belong to a low-rank dimensional space. This work introduces the use of the low-rank matrix approximation as a regularisation prior for galaxy image deconvolution and compares its performance with a standard sparse regularisation technique. This new approach leads to a natural way to handle a space variant PSF. Deconvolution is performed using a Python code that implements a primal-dual splitting algorithm. The data set considered is a sample of 10 000 space-based galaxy images convolved with a known spatially varying Euclid-like PSF and including various levels of Gaussian additive noise. Performance is assessed by examining the deconvolved galaxy image pixels and shapes. The results demonstrate that the low-rank method performs as a well as sparsity for small samples of galaxies and outperforms sparsity for larger samples.

This presentation is part of Minisymposium “MS9 - Innovative models and algorithms for astronomical imaging (2 parts)”
organized by: Silvia Tozza (INdAM/Dept. Mathematics, University of Rome “La Sapienza”) , Marco Castellano (INAF Osservatorio Astronomico di Roma) , Maurizio Falcone (Dipartimento di Matematica, Università di Roma "La Sapienza") , Adriano Fontana (INAF Osservatorio Astronomico di Roma) .

Authors:

Jean-Luc Starck (Service d’Astrophysique, CEA Saclay)

Morgan Schmitz (CEA)

Samuel Farrens (CEA)

Keywords:

blind deconvolution, image deblurring, image reconstruction, inverse problems, psf field recovery, sparsity, statistical inverse estimation methods