  Image restoration in astronomy has been considered a vital step in many
ground-based observational programs that often suffer from sub-optimal seeing
due to atmospheric turbulence, distortion of stellar shapes due to instrumental
aberrations, trailing, and other issues. It holds importance for various tasks:
improved astrometry, deblending of overlapping sources, faint source detection,
and identification of point sources near bright extended objects, such as
galaxies, to name a few. We conduct an empirical study by applying the Scaled
Gradient Projection (SGP) iterative image deconvolution algorithm to restore
distorted stellar shapes in our observed data. We investigate using a more
flexible divergence measure, the $\beta$-divergence, which contains the
commonly-used Kullback-Leibler (KL) divergence as a special case and allows
automatic adaptation of the parameter $\beta$ to the data. An extensive set of
experiments comparing the performance of SGP and its $\beta$-divergence variant
($\beta$-SGP) is carried out on extracted star stamps and on images containing
multiple stars (both crowded and relatively sparser fields). We show a
consistent enhancement in the flux conservation across all considered scenarios
using $\beta$-SGP compared to SGP. Using a few quantifiable metrics such as the
Full-Width-at-Half-Maximum (FWHM) and ellipticity of stars, we observe that
$\beta$-SGP improves restoration quality, compared to the SGP, in many cases
and still preserves restoration quality in others. We conclude that generalized
versions of image restoration algorithms are more robust due to their enhanced
flexibility and could be a promising modification for astronomical image
restoration.
