Primordial B-mode detection is one of the main goals of current and future cosmic microwave background (CMB) experiments. However, the weak B-mode signal is overshadowed by several Galactic polarized emissions, such as thermal dust emission and synchrotron radiation. Subtracting foreground components from CMB observations is one of the key challenges in searching for the primordial B-mode signal. Here, we construct a deep convolutional neural network (CNN) model, called CMBFSCNN (Cosmic Microwave Background Foreground Subtraction with CNN), which can cleanly remove various foreground components from simulated CMB observational maps at the sensitivity of the CMB-S4 experiment. Noisy CMB Q (or U) maps are recovered with a mean absolute difference of 0.018 ± 0.023 μK (or 0.021 ± 0.028 μK). To remove the residual instrumental noise from the foreground-cleaned map, inspired by the needlet internal linear combination method, we divide the whole data set into two “half-split maps,” which share the same sky signal, but have uncorrelated noise, and perform a cross-correlation technique to reduce the instrumental noise effects at the power spectrum level. We find that the CMB EE and BB power spectra can be precisely recovered with significantly reduced noise effects. Finally, we apply this pipeline to current Planck observations. As expected, various foregrounds are cleanly removed from the Planck observational maps, with the recovered EE and BB power spectra being in good agreement with the official Planck results.

Primordial B-mode detection is one of the main goals of next-generation cosmic microwave background (CMB) experiments. Primordial B-modes are a unique signature of primordial gravitational waves (PGWs). However, the gravitational interaction of CMB photons with large-scale structures will distort the primordial E modes, adding a lensing B-mode component to the primordial B-mode signal. Removing the lensing effect (“delensing”) from observed CMB polarization maps will be necessary to improve the constraint of PGWs and obtain a primordial E-mode signal. Here, we introduce a deep convolutional neural network model named multi-input multi-output U-net (MIMO-UNet) to perform CMB delensing. The networks are trained on simulated CMB maps with size 20° × 20°. We first use MIMO-UNet to reconstruct the unlensing CMB polarization (Q and U) maps from observed CMB maps. The recovered E-mode power spectrum exhibits excellent agreement with the primordial EE power spectrum. The recovery of the primordial B-mode power spectrum for noise levels of 0, 1, and 2 μK-arcmin is greater than 98% at the angular scale of ℓ < 150. We additionally reconstruct the lensing B map from observed CMB maps. The recovery of the lensing B-mode power spectrum is greater than roughly 99% at the scales of ℓ > 200. We delens the observed B-mode power spectrum by subtracting the reconstructed lensing B-mode spectrum. The recovery of tensor B-mode power spectrum for noise levels of 0, 1, and 2 μK-arcmin is greater than 98% at the angular scales of ℓ < 120. Even at ℓ = 160, the recovery of tensor B-mode power spectrum is still around 71%.

The lensing effect of the cosmic microwave background (CMB) is a powerful tool for our study of the distribution of matter in the universe. The quadratic estimator (QE) method, which is widely used to reconstruct lensing potential, has been known to be suboptimal for the low noise level polarization data from next-generation CMB experiments. To improve the performance of the reconstruction, other methods, such as the maximum-likelihood estimator and machine-learning algorithms, have been developed. In this work, we present a deep convolutional neural network model named the Residual Dense Local Feature U-net (RDLFUnet) for reconstructing the CMB lensing convergence field. By simulating lensed CMB data with different noise levels to train and test network models, we find that for noise levels less than 5 μK-arcmin, RDLFUnet can recover the input gravitational potential with a higher signal-to-noise ratio than the previous deep-learning and traditional QE methods at almost the entire observation scale.