Upcoming radio interferometers are aiming to image the sky at new levels of resolution and sensitivity, with wide-band image cubes reaching close to the Petabyte scale for SKA. Modern proximal optimization algorithms have shown a potential to significantly outperform CLEAN thanks to their ability to inject complex image models to regularize the inverse problem for image formation from visibility data. They were also shown to be scalable to large data volumes thanks to a splitting functionality enabling the decomposition of data into blocks, for parallel processing of block-specific data-fidelity terms of the objective function. In this work, the splitting functionality is further exploited to decompose the image cube into spatio-spectral facets, and enable parallel processing of facet-specific regularization terms in the objective. The resulting Faceted HyperSARA algorithm is implemented in MATLAB (code available on GitHub). Simulation results on synthetic image cubes confirm that faceting can provide a major increase in scalability at no cost in imaging quality. A proof-of-concept reconstruction of a 15 GB image of Cyg A from 7.4 GB of VLA data, utilizing 496 CPU cores on a HPC system for 68 hours, confirms both scalability and a quantum jump in imaging quality from CLEAN. Assuming slow spectral slope of Cyg A, we also demonstrate that Faceted HyperSARA can be combined with a dimensionality reduction technique, enabling utilizing only 31 CPU cores for 142 hours to form the Cyg A image from the same data, while preserving reconstruction quality. Cyg A reconstructed cubes are available online.

Variational-based methods are the state-of-the-art in sparse image deconvolution. Yet, this class of methods might not scale to large dimensions of interest in current high resolution imaging applications. To overcome this limitation, we propose to solve the sparse deconvo-lution problem through a two-step approach consisting in first solving (approximately and fast) an optimization problem following by a neural network for "Deep Post Processing" (DPP). We illustrate our method in radio astronomy, where algorithms scalability is paramount due to the extreme data dimensions. First results suggest that DPP is able to achieve similar quality to state-of-the-art methods in a fraction of the time.