  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, standard methods in radio
interferometry produce reconstructed interferometric images that are limited in
quality and they are not scalable 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. We apply PURIFY to real interferometric observations. For all
observations PURIFY outperforms the standard CLEAN, where in some cases PURIFY
provides an improvement in dynamic range by over an order of magnitude. The
latest version of PURIFY, which includes the developments presented in this
work, is made publicly available.
