Multiscale feature integration network for inpainting of full-sky CMB $B$-modes

TL;DR

This work tackles incomplete sky coverage and E/B leakage in CMB polarization analyses by introducing SkyReconNet-P, a region-based, multiscale CNN that jointly reconstructs $(Q,U)$ on masked skies. It evaluates map- and spectrum-level fidelity under two masks and uses a simulation-based linear calibration to correct multipole-dependent $B$-mode biases, enabling unbiased inference of $r$ and $A_{ m lens}$ from reconstructed spectra. The approach demonstrates that inpainting can preserve the information needed for downstream pipelines and can outperform pseudo-$C_\ell$-based methods in certain regimes. This provides a practical, quantitative pathway for integrating ML-driven gap filling into cosmological analysis of future CMB polarization data.

Abstract

Foreground masking and incomplete sky coverage complicate CMB polarization analyses by inducing mode coupling and imperfect E/B separation, with particularly strong impact on searches for primordial $B$-modes. We present SkyReconNet-P, a convolutional neural network for inpainting CMB polarization maps that extends the SkyReconNet framework to jointly reconstruct the polarization $(Q,U)$ maps from partial-sky observations. The method combines regional processing with a hybrid design, utilizing standard convolution and dilated convolution to do a multiscale feature integration. We evaluate performance at both the map and power spectrum level using two masking scenarios: a generated random mask and the Planck 2018 common polarization inpainting mask. For both masking scenarios, SkyReconNet-P reproduces the large-scale morphology of the target maps. In power-spectrum space, we find that the reconstructed $E$-mode spectrum closely tracks the target at low multipoles, while small biases emerge at higher $\ell$. For $B$-mode, the raw reconstructed spectra exhibit a larger multipole-dependent bias, which we mitigate using a simulation-based linear calibration. We show that the calibrated $B$-mode spectrum preserve more information by comparing it with spectrum estimation using pseudo-$C_\ell$. Finally, we demonstrate cosmological parameter inference from calibrated reconstructed spectra by fitting $(r, A_{\rm lens})$ with a Gaussian bandpower likelihood, recovering posteriors consistent with injected parameters across three test ensembles down to $r \sim 10^{-3}$. These results support inpainting as a complementary route to cut-sky approaches when downstream pipelines can greatly benefit from statistically well-characterized, gap-filled polarization maps.

Figures (11)

• Figure 1: Three-panel view of $Q$ (top) and $U$ (bottom) polarization maps from the trained network with the generated mask. From left to right: target (unmasked) map, reconstructed map, and the residual (reconstructed minus target).
• Figure 2: E-mode angular power spectrum for the trained network with the generated mask. The upper panel shows $D_\ell^{EE}$ from the target (grey) and reconstructed (coloured) maps on the masked sky. The lower panel shows the percentage difference between the two. The reconstruction tracks the target spectrum closely at low multipoles, with an increasing negative bias for $\ell \gtrsim 60$.
• Figure 3: $B$-mode angular power spectrum for the same realization ($r = 0.00022$). The upper panel compares the target $D_\ell^{BB}$, the raw reconstructed spectrum (magenta), and the BB-calibrated spectrum (green) obtained using the amplitude-correction model described in the text. The lower panel shows the corresponding percentage differences with respect to the target. The calibration substantially reduces the mean bias in $D_\ell^{BB}$ over the analysis range, leaving predominantly realization-to-realization fluctuations.
• Figure 4: Three-panel view of $Q$ (top) and $U$ (bottom) polarization maps from the trained network with the Planck mask. From left to right: target (unmasked) map, reconstructed map, and the residual (reconstructed minus target).
• Figure 5: E-mode angular power spectrum for the trained network with the Planck mask. The upper panel shows $D_\ell^{EE}$ from the target (grey) and reconstructed (coloured) maps on the masked sky, and the lower panel shows the percentage difference between the two. The reconstruction tracks the target spectrum closely at low multipoles, with an increasing negative bias for $\ell \gtrsim 60$.