Lensing reconstruction from Planck sky maps: inhomogeneous noise

We discuss the effects of inhomogeneous sky coverage on cosmic microwave background lens reconstruction, focusing on application to the recently launched Planck satellite. We discuss the 'mean field' which is induced by noise inhomogeneities, as well as three approaches to lens reconstruction in this context: an optimal maximum-likelihood approach which is computationally expensive to evaluate and two suboptimal approaches which are less intensive. The first of these is only suboptimal at the 5 per cent level for Planck, and the second prevents biasing due to uncertainties in the noise model.