Co-addition and Subtraction of Undersampled Images

In astronomical imaging surveys, repeated observations of the same sky patches are taken in order to obtain deeper images and detect new sources. This is the case in the search for many transient phenomena, such as supernovae, gravitational wave (GW) optical counterparts and other cataclysmic variables. In many such surveys some of the images are undersampled, meaning that the pixel size is too large, and the image suffers from aliasing. For undersampled images, both co-addition of the images and background subtraction are done in a non-optimal manner, which leads to reduced sensitivity and an increased rate of false alarms. We present a new method (named Linear Undersampled Transients \& Addition (LUTRA)) that performs both processes in a mathematically proven optimal way, which allows improved performance for many scientific applications. It also allows easy and direct performance of measurements such as photometry and astrometry in a simple manner, while providing results in super-resolution. We demonstrate the performance of the method on public ZTF data and show $\times 1.25$ higher SNR compared to current methods. We provide an open source Python implementation.