Unlocking ultra-deep wide-field imaging with sidereal visibility averaging

Producing ultra-deep high-angular-resolution images with current and next-generation radio interferometers introduces significant computational challenges. In particular, the imaging is so demanding that processing large datasets, accumulated over hundreds of hours on the same pointing, is likely infeasible in the current data reduction schemes. In this paper, we revisit a solution to this problem that was considered in the past but is not being used in modern software: sidereal visibility averaging (SVA). This technique combines individual observations taken at different sidereal days into one much smaller dataset by averaging visibilities at similar baseline coordinates. We present our method and validated it using four separate 8-hour observations of the ELAIS-N1 deep field, taken with the International LOw Frequency ARray (LOFAR) Telescope (ILT) at 140~MHz. Additionally, we assessed the accuracy constraints imposed by Earth's orbital motion relative to the observed pointing when combining multiple datasets. We find, with four observations, data volume reductions of a factor of 1.8 and computational time improvements of a factor of 1.6 compared to standard imaging. These factors will increase when more observations are combined with SVA. For instance, with 3000~hours of LOFAR data aimed at achieving sensitivities of the order of {\mu}Jy/beam at sub-arcsecond resolutions, we estimate data volume reductions of up to a factor of 169 and a 14-fold decrease in computing time using our current algorithm. This advancement for imaging large deep interferometric datasets will benefit current generation instruments, such as LOFAR, and upcoming instruments such as the Square Kilometre Array (SKA), provided the calibrated visibility data of the individual observations are retained.