  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 l21
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.
