Polca SARA - Full polarization, direction-dependent calibration and sparse imaging for radio interferometry.

New generation of radio interferometers arc envisaged to produce high quality, high dynamic range Stokes images of the observed sky from the corresponding undersampled Fourier domain measurements. In practice, these measurements are contaminated by the instrumental and atmospheric effects that are well represented by Jones matrices, and are most often varying with observation direction and time. These effects, usually unknown, act as a limiting factor in achieving the required imaging performance and thus, their calibration is crucial. To address this issue, we develop a global algorithm, named Polca SARA, aiming to perform full polarization, direction-dependent calibration, and sparse imaging by employing a non-convex optimization technique. In contrast with the existing approaches, the proposed method offers global convergence guarantees and flexibility to incorporate sophisticated priors to regularize the imaging as well as the calibration problem. Thus, we adapt a polarimetric imaging specific method, enforcing the physical polarization constraint along with a sparsity prior for the sought images. We perform extensive simulation studies of the proposed algorithm. The results indicate the superior performance of polarization constraint based imaging when combined with the calibration of the direction-dependent effects for full Jones matrices, including their off-diagonal terms (denoting polarization leakage). The chosen priors in the proposed approach are also shown to handle the unitary ambiguity problem to a good extent.