# Maximum a posteriori CMB lensing reconstruction

## TL;DR

This paper introduces LensIt, an efficient iterative method for maximum a posteriori CMB lensing reconstruction that significantly improves signal-to-noise ratio over quadratic estimators, especially for polarization data.

## Contribution

The authors develop and implement LensIt, a novel algorithm that finds the most probable lensing map without significant approximations, enhancing the accuracy of CMB lensing reconstruction.

## Key findings

- LensIt achieves maximal theoretical improvement in signal-to-noise ratio.
- Delensing with LensIt reduces tensor-to-scalar ratio errors by about a factor of 2.
- The method is efficient, converging quickly with linear computational cost.

## Abstract

Gravitational lensing of the CMB is a valuable cosmological signal that correlates to tracers of large-scale structure and acts as a important source of confusion for primordial $B$-mode polarization. State-of-the-art lensing reconstruction analyses use quadratic estimators, which are easily applicable to data. However, these estimators are known to be suboptimal, in particular for polarization, and large improvements are expected to be possible for high signal-to-noise polarization experiments. We develop a method and numerical code, $\rm{LensIt}$, that is able to find efficiently the most probable lensing map, introducing no significant approximations to the lensed CMB likelihood, and applicable to beamed and masked data with inhomogeneous noise. It works by iteratively reconstructing the primordial unlensed CMB using a deflection estimate and its inverse, and removing residual lensing from these maps with quadratic estimator techniques. Roughly linear computational cost is maintained due to fast convergence of iterative searches, combined with the local nature of lensing. The method achieves the maximal improvement in signal to noise expected from analytical considerations on the unmasked parts of the sky. Delensing with this optimal map leads to forecast tensor-to-scalar ratio parameter errors improved by a factor $\simeq 2 $ compared to the quadratic estimator in a CMB stage IV configuration.