Deblurring Galaxy Images with Tikhonov Regularization on Magnitude Domain

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 ).