Real space estimator for the weak lensing convergence from the CMB

We propose an estimator defined in real space for the reconstruction of the weak lensing potential due to the intervening large scale structure from high resolution maps of the cosmic microwave background. This estimator was motivated as an alternative to the quadratic estimator in harmonic space to surpass the difficulties of the analysis of maps containing galactic cuts and point source excisions. Using maps synthesised by pixel remapping, we implement the estimator for two experiments, namely one in the absence and one in the presence of detector noise, and compare the reconstruction of the convergence field with that obtained with the quadratic estimator defined in harmonic space. We find good agreement between the input and the reconstructed power spectra using the proposed real space estimator. We discuss interesting features of the real space estimator and future extensions of this work.