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

Radio interferometric (RI) data are noisy undersampled spatial Fourier components of the unknown radio sky affected by direction-dependent antenna gains. Failure to model these antenna gains accurately results in a radio sky estimate with limited fidelity and resolution. The RI inverse problem has been recently addressed via a joint calibration and imaging approach that consists in solving a non-convex minimization task, involving suitable priors for the direction-dependent effects (DDEs), namely temporal and spatial smoothness, and sparsity for the unknown radio map via an l(1)-norm prior, in the context of realistic RI simulations. Building on these developments, we propose to promote sparsity of the radio map via a log-sum prior, enforcing sparsity more strongly than the l(1) norm. The resulting minimization task is addressed via a sequence of non-convex minimization tasks composed of re-weighted l(1) image priors, which are solved approximately. We demonstrate the efficiency of the approach on RI observations of the celebrated radio galaxy Cygnus A obtained with the Karl G. Jansky Very Large Array at the frequency bands X, C, and S . More precisely, we showcase that the approach enhances data fidelity significantly while achieving high-resolution high-dynamic range radio maps, confirming the suitability of the priors considered for the unknown DDEs and radio image. As a clear qualitative indication of the high fidelity achieved by the data and the proposed approach, we report the detection of three background sources in the vicinity of Cyg A, at S band.