Real space lensing reconstruction using cosmic microwave background polarization

We develop a method of reconstructing the lensing field from lensed CMB temperature and polarization maps in real space as an alternative to the harmonic space estimators currently in use by extending an existing real space lensing estimator for temperature to polarization. Real space estimators have the advantage of being local in nature and they are thus equipped to deal with the nonuniform sky coverage, especially galactic cuts and point source excisions, found in experimental data. We characterize some of the properties and limitations of these estimators and test them on simulated maps with Planck, AdvACT and CMB-S4 noise. We show that the reconstructions for large-scale lensing fields are accurate, and that the polarization reconstructions improve on those from CMB temperature maps for future experiments as expected. High-fidelity lensing maps can be reconstructed with futuristic experiments like CMB-S4.