An iterative CMB lensing estimator minimizing instrumental noise bias

TL;DR

This paper tackles biases in CMB lensing reconstruction arising from anisotropic instrumental noise. It extends the MAP lensing formalism by introducing a cross-only iterative estimator that uses split maps with independent noise to suppress auto-correlations, reducing mean-field and $N_L^{(0)}$ biases with negligible loss in signal-to-noise in the many-splits limit. The authors derive a cross-only gradient, a corresponding loss function, and a practical iterative recipe, including Monte Carlo normalization and mean-field treatment. Validation with simulations across ACT-like, SO-like, and CMB-S4-like configurations demonstrates substantial suppression of noise biases and mean-field, especially for polarization-based reconstructions, with only modest increases in bandpower variance. The approach offers a robust and near-optimal path for next-generation CMB lensing analyses and suggests avenues to extend QE techniques within the MAP framework for broader applicability.

Abstract

Noise maps from CMB experiments are generally statistically anisotropic, due to scanning strategies, atmospheric conditions, or instrumental effects. Any mis-modeling of this complex noise can bias the reconstruction of the lensing potential and the measurement of the lensing power spectrum from the observed CMB maps. We introduce a new CMB lensing estimator based on the maximum a posteriori (MAP) reconstruction that is minimally sensitive to these instrumental noise biases. By modifying the likelihood to rely exclusively on correlations between CMB map splits with independent noise realizations, we minimize auto-correlations that contribute to biases. In the regime of many independent splits, this maximum closely approximates the optimal MAP reconstruction of the lensing potential. In simulations, we demonstrate that this method is able to determine lensing observables that are immune to any noise mis-modeling with a negligible cost in signal-to-noise ratio. Our estimator enables unbiased and nearly optimal lensing reconstruction for next-generation CMB surveys.

Figures (5)

• Figure 1: Biases of the MAP and cross-only MAP estimators for our three experimental configurations. The mean biases obtained from 200 simulations with the MAP and cross-only MAP estimators are shown as the circles and squares, respectively. The solid and dotted lines are the predictions of the $N_L^{(0)}$ and $N_L^{(1)}$ biases for the MAP and the cross-only MAP estimators, respectively. The dashed lines are the residual biases obtained from 100 noiseless simulations with the standard (co-add) MAP estimator for each experimental configuration. The black solid line is the fiducial CMB lensing power spectrum. We show ACT-like temperature (orange), SO-like for temperature and for both temperature and polarization (purple and sky blue) and CMB-S4-like polarization (teal). We see that the CMB-S4 polarization configuration benefits the most from the bias reduction from the split estimator, while when the CMB fields are signal dominated, such as for the SO temperature case, the bias is less significantly reduced. Note that this bias reduction does not correspond to a reduction in the variance of the band-power estimates.
• Figure 2: Ratio of the CMB lensing power spectrum variance, for the cross-only estimators over the standard (co-add) MAP estimator, obtained from 200 full-sky simulations and binned in bandpowers. We show the cross-only QE (dashed lines) and cross-only MAP (solid lines), over the co-add MAP, for our three experimental configurations. For the SO-like case we show both the temperature-only and the temperature and polarization estimators. The variance of the cross-only estimators are always higher than the co-add MAP estimator, as expected. We see that the increase in variance of the cross-only QE is greatly reduced for the cross-only MAP estimator, in particular for surveys including polarization. Comparing the cross-only MAP to the co-add MAP, we see that the increase in variance is below $5\%$ for the ACT-like and SO-like configurations. For the CMB-S4 case, at multipoles $L<1000$, where most of the signal-to-noise is accumulated, the degradation is still negligible.
• Figure 3: Correlation matrices for the lensing power spectrum $C^{\phi\phi}_L$ in 25 bins between $L=2$ and $L=3000$. We show the standard MAP in the upper-left triangles, and the cross-only MAP in the lower-right triangles, for the four experimental configurations considered. We see that in the CMB-S4 polarization configuration, the cross-only covariance is visibly more diagonal than the standard MAP. Note that no realisation-dependent bias correction is made, which would significantly reduce the off-diagonal correlations.
• Figure 4: One realization of the noise map used for the simulations, following the Planck scanning strategy, scaled such that the its standard deviation is of $10\,\mu\text{K-arcmin}$.
• Figure 5: Power spectra of the mean-field for the QE (orange), standard MAP (blue) and cross-only MAP (teal), estimated from averaging over 100 simulations with anisotropic noise patterns. The QE cross-only mean-field is zero by construction. For reference we show the fiducial lensing power spectrum (solid black line) and the $N_L^{(0), \rm MAP}$ bias (dashed black line). The left panel is for the ACT-like configuration with temperature, the central panel is for a SO-like configuration with temperature, and the right panel is for CMB-S4 with polarization. We see that the cross-only MAP is able to reduce the mean-field term, in particular in the polarization CMB-S4 configuration. The mean-field does not disappear in the temperature only reconstructions, but it is reduced by an order of magnitude for both ACT and SO. We also show the predicted mean-field power spectrum due to noise anisotropies as the dotted and dashed lines, for standard QE and MAP estimators, respectively.