$w$-stacking $w$-projection hybrid algorithm for wide-field interferometric imaging: implementation details and improvements

We present a detailed discussion of the implementation strategies for a recently developed $w$-stacking $w$-projection hybrid algorithm used to reconstruct wide-field interferometric images. In particular, we discuss the methodology used to deploy the algorithm efficiently on a supercomputer via use of a Message Passing Interface (MPI) $k$-means clustering technique to achieve efficient construction and application of non co-planar effects. Additionally, we show that the use of conjugate symmetry increases the algorithms performance by imaging an interferometric observation of Fornax A from the Murchison Widefield Array (MWA). We perform exact non-coplanar wide-field correction for 126.6 million visibilities using 50 nodes of a computing cluster. The $w$-projection kernel construction takes only 15 minutes, demonstrating that the implementation is both fast and efficient.