A New PSF Deconvolution Algorithm: Simultaneous Spatial Resolution Enhancement and Point Source Removal for Morphological Analysis of AGN Host Galaxies

We propose a new point-spread function (PSF) deconvolution algorithm for images of galaxies hosting an active galactic nucleus (AGN), designed to simultaneously enhance the spatial resolution of the host galaxy and remove the bright central point source. In this algorithm, an intrinsic image is reconstructed by decomposing an observed image into two components: an image $I_{\rm sm}$ of an extended component (i.e., a host galaxy) and an image $I_{\rm sp}$ of a point-source component (i.e., an AGN). During image reconstruction, three constraints are imposed: (1) a smooth constraint on the image $I_{\rm sm}$ , which spatially smooths the host-galaxy structures; (2) a sparse constraint on the image $I_{\rm sp}$ , which localizes the point source to a small number of pixels; and (3) a new constraint, the point-source balance constraint, based on the pixel-wise product $I_{\rm sm} \times I_{\rm sp}$ , which removes the point source from the host galaxy without over- or under-subtraction. As a test, we apply this algorithm to images of artificial and $z \sim 0-1$ real AGNs observed with Hyper Suprime-Cam on the Subaru Telescope. We find that the spatial resolution of the host-galaxy images is improved to a level comparable to that of images from the Hubble Space Telescope and that the bright central point sources are removed. This algorithm is expected to enable statistical morphological studies of distant AGN host galaxies when applied to wide-field survey data from the Vera C. Rubin Observatory, the Euclid Space Telescope, and the Roman Space Telescope.