  We propose a regularization-based deblurring method that works efficiently
for galaxy images. The spatial resolution of a ground-based telescope is
generally limited by seeing conditions and much worse than space-based
telescopes. This circumstance has generated considerable research interest in
restoration of spatial resolution. Since image deblurring is a typical inverse
problem and often ill-posed, solutions tend to be unstable. To obtain a stable
solution, much research has adopted regularization-based methods for image
deblurring, but the regularization term is not necessarily appropriate for
galaxy images. Although galaxies have an exponential or Sersic profile, the
conventional regularization assumes the image profiles to behave linear in
space. The significant deviation between the assumption and real situation
leads to blurring the images and smoothing out the detailed structures.
Clearly, regularization on logarithmic, i.e. magnitude domain, should provide a
more appropriate assumption, which we explore in this study. We formulate a
problem of deblurring galaxy images by an objective function with a Tikhonov
regularization term on magnitude domain. We introduce an iterative algorithm
minimizing the objective function with a primal-dual splitting method. We
investigate the feasibility of the proposed method using simulation and
observation images. In the simulation, we blur galaxy images with a realistic
point spread function and add both Gaussian and Poisson noises. For the
evaluation with the observed images, we use galaxy images taken by the Subaru
HSC-SSP. Both of these evaluations show that our method successfully recovers
the spatial resolution of the images and significantly outperforms the
conventional methods. The code is publicly available from the Github (
https://github.com/kzmurata-astro/PSFdeconv_amag ).
