An improved method for polarimetric image restoration in interferometry
Interferometric radio astronomy data require the effects of limited coverage in the Fourier plane to be accounted for via a deconvolution process. For the last 40 years this process, known as `cleaning', has been performed almost exclusively on all Stokes parameters individually as if they were independent scalar images. However, here we demonstrate for the case of the linear polarisation $\mathcal{P}$, this approach fails to properly account for the complex vector nature resulting in a process which is dependant on the axis under which the deconvolution is performed. We present here an improved method, `Generalised Complex CLEAN', which properly accounts for the complex vector nature of polarised emission and is invariant under rotations of the deconvolution axis. We use two Australia Telescope Compact Array datasets to test standard and complex CLEAN versions of the Högbom and SDI CLEAN algorithms. We show that in general the Complex CLEAN version of each algorithm produces more accurate clean components with fewer spurious detections and lower computation cost due to reduced iterations than the current methods. In particular we find that the Complex SDI CLEAN produces the best results for diffuse polarised sources as compared with standard CLEAN algorithms and other Complex CLEAN algorithms. Given the move to widefield, high resolution polarimetric imaging with future telescopes such as the Square Kilometre Array, we suggest that Generalised Complex CLEAN should be adopted as the deconvolution method for all future polarimetric surveys and in particular that the complex version of a SDI CLEAN should be used.