Maximum a posteriori CMB lensing reconstruction

Abstract

Gravitational lensing of the cosmic microwave background (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, 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 ≃2 compared to the quadratic estimator in a CMB stage IV configuration.

Internal Delensing of Cosmic Microwave Background Polarization B -Modes with the POLARBEAR Experiment

“…We report here a delensing analysis of the sub-degree B-mode signal angular power spectrum C BB of the CMB polarization experiment POLARBEAR [15,16]. We test two types of internal lensing estimators: the standard quadratic estimator (QE)φ QE [17] and a more powerful maximum a posteriori (MAP) iterative method φ MAP [14,18], applied here to data for the first time. CMB-internal lensing estimators cannot differentiate between the true effect of lensing or features originating from random CMB and noise fluctuations.…”

“…The construction of the MAP lensing estimate follows closely Ref. [18], with the addition of OBD and a simpler treatment of the mean-field. At each iteration step, the filter in Eq.…”

Optimal filtering for CMB lensing reconstruction

“…Since the noise and unlensed CMB are expected to be Gaussian, and lensing simply deflects points on the sky, it is straightforward to write down a likelihood for the observed CMB given a fixed lensing deflection field. The lensing potential is also Gaussian to a good approximation on most relevant scales, so finding the lensing potential that maximizes the posterior then gives an optimal estimator for the lensing potential [8,9]. The resulting estimator is a complicated nonlinear function of observed fields that has to be evaluated iteratively, but can be approximated to good accuracy for the near future by a quadratic estimator (QE) that is easier to evaluate [10][11][12].…”

“…Although we have demonstrated significant gains compared to simple QE estimators, our results are clearly not fully optimal both because of approximations in the κ-filtering and because the estimator is still fundamentally quadratic. A likelihood based approach using iterative estimators [8,9] could perform substantially better in the high signal-tonoise regime where quadratic estimators become suboptimal. However, a fully optimal power spectrum estimator applicable to realistic cut-sky data with inhomogeneous noise does not currently exist, and developing such an estimator would be an interesting avenue for future research.…”

Exploring cosmic origins with CORE: Gravitational lensing of the CMB

“…The noise levels on reconstructions that properly maximise the posterior distribution of φ given the observed CMB fields have been shown (in simulations; e.g., ref. [40]) to be well reproduced by an approximate iterative calculation of the noise power N (0) l of the quadratic estimator [42]. Here, we use the implementation described in ref.…”