  Next-generation radio interferometers, such as the Square Kilometre Array
(SKA), will revolutionise our understanding of the universe through their
unprecedented sensitivity and resolution. However, to realise these goals
significant challenges in image and data processing need to be overcome. The
standard methods in radio interferometry for reconstructing images, such as
CLEAN, have served the community well over the last few decades and have
survived largely because they are pragmatic. However, they produce
reconstructed inter\-ferometric images that are limited in quality and
scalability for big data. In this work we apply and evaluate alternative
interferometric reconstruction methods that make use of state-of-the-art sparse
image reconstruction algorithms motivated by compressive sensing, which have
been implemented in the PURIFY software package. In particular, we implement
and apply the proximal alternating direction method of multipliers (P-ADMM)
algorithm presented in a recent article. First, we assess the impact of the
interpolation kernel used to perform gridding and degridding on sparse image
reconstruction. We find that the Kaiser-Bessel interpolation kernel performs as
well as prolate spheroidal wave functions, while providing a computational
saving and an analytic form. Second, we apply PURIFY to real interferometric
observations from the Very Large Array (VLA) and the Australia Telescope
Compact Array (ATCA) and find images recovered by PURIFY are higher quality
than those recovered by CLEAN. Third, we discuss how PURIFY reconstructions
exhibit additional advantages over those recovered by CLEAN. The latest version
of PURIFY, with developments presented in this work, is made publicly
available.
