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Radio interferometric (RI) data are noisy under-sampled spatial Fouriercomponents of the unknown radio sky affected by direction-dependent antennagains. Failure to model these antenna gains accurately results in a radio skyestimate with limited fidelity and resolution. The RI inverse problem has beenrecently addressed via a joint calibration and imaging approach which consistsin solving a non-convex minimisation task, involving suitable priors for theDDEs, namely temporal and spatial smoothness, and sparsity for the unknownradio map via an $\ell_1$-norm prior, in the context of realistic RIsimulations. Building on these developments, we propose to promote sparsity ofthe radio map via a log-sum prior, enforcing sparsity more strongly than the$\ell_1$-norm. The resulting minimisation task is addressed via a sequence ofnon-convex minimisation tasks composed of re-weighted $\ell_1$ image priors,which are solved approximately. We demonstrate the efficiency of the approachon RI observations of the celebrated radio galaxy Cygnus~A obtained with theKarl G. Jansky Very Large Array at X, C, and S bands. More precisely, weshowcase that the approach enhances data fidelity significantly while achievinghigh resolution high dynamic range radio maps, confirming the suitability ofthe priors considered for the unknown DDEs and radio image. As a clearqualitative indication of the high fidelity achieved by the data and theproposed approach, we report the detection of three background sources in thevicinity of Cyg~A, at S band.

Cygnus A jointly calibrated and imaged via non-convex optimisation from VLA data