Optimal filtering for CMB lensing reconstruction

Abstract

Upcoming ground-based cosmic microwave background experiments will provide CMB maps with high sensitivity and resolution that can be used for high fidelity lensing reconstruction. However, the sky coverage will be incomplete and the noise highly anisotropic, so optimized estimators are required to extract the most information from the maps. We focus on quadratic-estimator based lensing reconstruction methods that are fast to implement, and compare new more-optimally filtered estimators with various estimators that have previously been used in the literature. Input CMB maps can be optimally inverse-signal-plus-noise filtered using conjugate gradient (or other) techniques to account for the noise anisotropy. However, lensing reconstructions from these filtered input maps have an anisotropic response to the lensing signal and are difficult to interpret directly. We describe a second-stage filtering of the lensing maps and analytic response model that can be used to construct lensing power spectrum estimates that account for the anisotropic response and noise inhomogeneity in an approximately optimal way while remaining fast to compute. We compare results for simulations of upcoming Simons Observatory and CMB Stage-4 experiments to show the robustness of the more optimal lensing reconstruction pipeline and quantify the improvement compared to less optimal estimators. We find a substantial improvement in reconstructed lensing power variance between optimal anisotropic and isotropic filtering of CMB maps, and up to 30% improvement in variance by using the additional filtering step on the reconstruction potential map. Our approximate analytic response model is unbiased to within a small percentlevel additional Monte Carlo correction.

Instrumental systematics biases in CMB lensing reconstruction: A simulation-based assessment

“…We perform a flatsky quadratic estimator (QE) lensing reconstruction using the pipeline presented in Ref. [12]. After performing the standard quadratic estimator lensing reconstruction, this analysis also includes a filtering step applied to the reconstructed lensing field, which is designed to approximately minimize the corresponding power spectrum errors.…”

“…This is then filtered using the effective patch-approximated response R κ eff , the reconstruction noise N κ 0,eff (see Ref. [12]) and a fiducial κ spectrum C κκ fid , to definê…”

“…is the required normalization for our analytic patch approximation estimator [12]. f p is the fraction of the map area in patch p. The MF is calculated twice, from two sets of 48 MC simulations.…”

“…We assume a realistic amplitude for the modeled systematics, as observed in the current generation of experiments, or as expected for the next generation instruments given their design specifications. Our baseline reconstruction pipeline performs a semioptimal treatment of noise inhomogeneities induced by the scanning strategies of ground-based experiments [12], however it does not automatically mitigate possible residual systematic biases. Using systematics-free Monte Carlo (MC) simulations to obtain the noise-debiasing terms for the CMB lensing power spectrum could lead to biases on real data.…”

CMB lensing reconstruction biases from masking extragalactic sources

“…The (optimal) filtering step produces Wiener-filtered maps that provide the minimum variance estimate of the full-sky lensed CMB based on the information in the unmasked area. Optimal filtering [72,75,76] is particularly valuable with this kind of mask compared to more basic (but faster) inverse-variance-weighted or isotropic filtering. Figure 5 shows how the optimal filtering operation is able to fill back some information inside small masked regions, effectively recovering information that was masked (assuming no residual foregrounds outside the masked area).…”