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Image restoration in astronomy has been considered a vital step in manyground-based observational programs that often suffer from sub-optimal seeingdue to atmospheric turbulence, distortion of stellar shapes due to instrumentalaberrations, 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 asgalaxies, to name a few. We conduct an empirical study by applying the ScaledGradient Projection (SGP) iterative image deconvolution algorithm to restoredistorted stellar shapes in our observed data. We investigate using a moreflexible divergence measure, the $\beta$-divergence, which contains thecommonly-used Kullback-Leibler (KL) divergence as a special case and allowsautomatic adaptation of the parameter $\beta$ to the data. An extensive set ofexperiments comparing the performance of SGP and its $\beta$-divergence variant($\beta$-SGP) is carried out on extracted star stamps and on images containingmultiple stars (both crowded and relatively sparser fields). We show aconsistent enhancement in the flux conservation across all considered scenariosusing $\beta$-SGP compared to SGP. Using a few quantifiable metrics such as theFull-Width-at-Half-Maximum (FWHM) and ellipticity of stars, we observe that$\beta$-SGP improves restoration quality, compared to the SGP, in many casesand still preserves restoration quality in others. We conclude that generalizedversions of image restoration algorithms are more robust due to their enhancedflexibility and could be a promising modification for astronomical imagerestoration.

$\beta$-SGP: Scaled Gradient Projection with $\beta$-divergence for astronomical image restoration