We leverage the Sparsity Averaging Reweighted Analysis (SARA) approach for interferometric imaging, that is based on convex optimisation, for the super-resolution of Cyg A from observations at the frequencies 8.422GHz and 6.678GHz with the Karl G. Jansky Very Large Array (VLA). The associated average sparsity and positivity priors enable image reconstruction beyond instrumental resolution. An adaptive Preconditioned Primal-Dual algorithmic structure is developed for imaging in the presence of unknown noise levels and calibration errors. We demonstrate the superior performance of the algorithm with respect to the conventional clean-based methods, reflected in super-resolved images with high fidelity. The high resolution features of the recovered images are validated by referring to maps of Cyg A at higher frequencies, more precisely 17.324GHz and 14.252GHz. We also confirm the recent discovery of a radio transient in Cyg A, revealed in the recovered images of the investigated data sets. Our matlab code is available online on GitHub.

We propose a new approach within the versatile framework of convex optimization to solve the radio-interferometric wideband imaging problem. Our approach, dubbed HyperSARA, solves a sequence of weighted nuclear norm and 2,1 minimization problems promoting low rankness and joint average sparsity of the wideband model cube. On the one hand, enforcing low rankness enhances the overall resolution of the reconstructed model cube by exploiting the correlation between the different channels. On the other hand, promoting joint average sparsity improves the overall sensitivity by rejecting artefacts present on the different channels. An adaptive Preconditioned Primal-Dual algorithm is adopted to solve the minimization problem. The algorithmic structure is highly scalable to large data sets and allows for imaging in the presence of unknown noise levels and calibration errors. We showcase the superior performance of the proposed approach, reflected in high-resolution images on simulations and real VLA observations with respect to single channel imaging and the clean-based wideband imaging algorithm in the wsclean software. Our matlab code is available online on github.

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.

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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 parallelizable over large data volumes thanks to a splitting functionality enabling the decomposition of the data into blocks, for parallel processing of block-specific data-fidelity terms involved in the objective function. Focusing on intensity imaging, the splitting functionality is further exploited in this work to decompose the image cube into spatio-spectral facets, and enable parallel processing of facet-specific regularization terms in the objective function, leading to the “Faceted HyperSARA” algorithm. Reliable heuristics enabling an automatic setting of the regularization parameters involved in the objective are also introduced, based on estimates of the noise level, transferred from the visibility domain to the domains where the regularization is applied. Simulation results based on a MATLAB implementation and involving synthetic image cubes and data close to Gigabyte size confirm that faceting can provide a major increase in parallelization capability when compared to the non-faceted approach (HyperSARA).