  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 the Euclid telescope. New surveys will provide
images containing thousand of galaxies and 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 for small samples of
galaxies sparsity performs better in terms of pixel and shape recovery, while
for larger samples of galaxies it is possible to obtain more accurate estimates
of the galaxy shapes using the low-rank approximation.
