Linear Image Regridding and Coaddition with Oversampled Point Spread Functions: Lessons from 1D

Image regridding and coaddition have a wide range of applications in astronomical observations. {\sc Imcom}, an algorithm that provides control over point spread function (PSF) and noise in coadded images, has been found to meet the stringent requirements of weak gravitational lensing cosmology with the forthcoming Nancy Grace Roman Space Telescope. In this work, I introduce a new algorithm, Fast {\sc Imcom}, which outperforms traditional {\sc Imcom} in terms of both efficiency and quality. After explaining the underlying philosophy and mathematical formalism, I conduct systematic comparisons between {\sc Imcom} and Fast {\sc Imcom} in terms of PSF reconstruction in 1D. While a 2D implementation is beyond the scope of this paper, I demonstrate how to generalize Fast {\sc Imcom} to 2D and discuss practical issues involved. This new algorithm has the potential of reducing both the computational costs and storage requirements (current estimates are $\sim 100\,{\rm M}$ core-hours and $\sim 1.5 \,{\rm PB}$, respectively) of the Roman High Latitude Imaging Survey (HLIS) by an order of magnitude. Meanwhile, it provides implications for the dithering patterns of Roman surveys (extrapolated from 1D to 2D). I also address potential applications of Fast {\sc Imcom} beyond the Roman HLIS, with focus on other weak lensing programs and Roman time domain surveys; the actual range of use cases is likely beyond what is discussed here.