Bayesian radio interferometric imaging with direction-dependent calibration

Context: Radio interferometers measure frequency components of the sky brightness, modulated by the gains of the individual radio antennas. Due to atmospheric turbulence and variations in the operational conditions of the antennas these gains fluctuate. Thereby the gains do not only depend on time but also on the spatial direction on the sky. To recover high quality radio maps an accurate reconstruction of the direction and time-dependent individual antenna gains is required. Aims: This paper aims to improve the reconstruction of radio images, by introducing a novel joint imaging and calibration algorithm including direction-dependent antenna gains. Methods: Building on the \texttt{resolve} framework, we designed a Bayesian imaging and calibration algorithm utilizing the image domain gridding method for numerically efficient application of direction-dependent antenna gains. Furthermore by approximating the posterior probability distribution with variational inference, our algorithm can provide reliable uncertainty maps. Results: We demonstrate the ability of the algorithm to recover high resolution high dynamic range radio maps from VLA data of the radio galaxy Cygnus A. We compare the quality of the recovered images with previous work relying on classically calibrated data. Furthermore we compare with a compressed sensing algorithm also incorporating direction-dependent gains. Conclusions: Including direction-dependent effects in the calibration model significantly improves the dynamic range of the reconstructed images compared to reconstructions from classically calibrated data. Compared to the compressed sensing reconstruction, the resulting sky images have a higher resolution and show fewer artifacts. For utilizing the full potential of radio interferometric data, it is essential to consider the direction dependence of the antenna gains.