How to Coadd Images. II. Anti-aliasing and PSF Deconvolution

Abstract: We have developed a novel method for co-adding multiple under-sampled images that combines the iteratively reweighted least squares and divide-and-conquer algorithms. Our approach not only allows for the anti-aliasing of the images but also enables Point-Spread Function (PSF) deconvolution, resulting in enhanced restoration of extended sources, the highest peak signal-to-noise ratio, and reduced ringing artefacts. To test our method, we conducted numerical simulations that replicated observation runs of the China Space Station Telescope/ the VLT Survey Telescope (VST) and compared our results to those obtained using previous algorithms. The simulation showed that our method outperforms previous approaches in several ways, such as restoring the profile of extended sources and minimizing ringing artefacts. Additionally, because our method relies on the inherent advantages of least squares fitting, it is more versatile and does not depend on the local uniformity hypothesis for the PSF. However, the new method consumes much more computation than the other approaches.