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We propose a new approach within the versatile framework of convexoptimization to solve the radio-interferometric wideband imaging problem. Ourapproach, dubbed HyperSARA, solves a sequence of weighted nuclear norm and l21minimization problems promoting low rankness and joint average sparsity of thewideband model cube. On the one hand, enforcing low rankness enhances theoverall resolution of the reconstructed model cube by exploiting thecorrelation between the different channels. On the other hand, promoting jointaverage sparsity improves the overall sensitivity by rejecting artefactspresent on the different channels. An adaptive Preconditioned Primal-Dualalgorithm is adopted to solve the minimization problem. The algorithmicstructure is highly scalable to large data sets and allows for imaging in thepresence of unknown noise levels and calibration errors. We showcase thesuperior performance of the proposed approach, reflected in high-resolutionimages on simulations and real VLA observations with respect to single channelimaging and the CLEAN-based wideband imaging algorithm in the WSCLEAN software.Our MATLAB code is available online on GITHUB.

Wideband Super-resolution Imaging in Radio Interferometry via Low Rankness and Joint Average Sparsity Models (HyperSARA)