Reconstruction of full sky CMB $\mathbf{E}$ and $\mathbf{B}$ modes spectra removing $\mathbf{E}$-to-$\mathbf{B}$ leakage from partial sky using deep learning

Abstract

Incomplete sky analysis of cosmic microwave background (CMB) polarization spectra poses a major problem of leakage between $E$- and $B$-modes. We present a machine learning approach to remove this $E$-to-$B$ leakage using a convolutional neural network (CNN) in presence of detector noise. The CNN predicts the full sky $E$- and $B$-modes spectra for multipoles $2\le \ell \le 384$ from the partial sky spectra for $N_{\mathrm{side}}=256$. We use tensor-to-scalar ratio $r=0.001$ to simulate the CMB polarization maps. We train our CNN using $10^5$ full sky target spectra and an equal number of noise contaminated partial sky spectra obtained from the simulated maps. The CNN works well for two masks covering the sky area of $\sim 80\%$ and $\sim 10\%$ respectively after training separately for each mask. For the assumed theoretical $E$- and $B$-modes spectra, predicted full sky $E$- and $B$-modes spectra agree well with the corresponding target spectra and their means agree with theoretical spectra. The CNN preserves the cosmic variances at each multipole, effectively removes correlations of the partial sky $E$- and $B$-modes spectra, and retains the entire statistical properties of the targets avoiding the problem of so-called $E$-to-$B$ leakage for the chosen theoretical model.

24 pages, 13 figures

References in corpus (9)

• COSMOPOWER: emulating cosmological power spectra for accelerated Bayesian inference from next-generation surveys
• A general solution to the E-B mixing problem
• Neural Network Reconstruction of Late-Time Cosmology and Null Tests
• Neural network reconstructions for the Hubble parameter, growth rate and distance modulus
• Reconstructing Cosmological Initial Conditions from Late-Time Structure with Convolutional Neural Networks
• Observational cosmology with Artificial Neural Networks
• Blind correction of the EB-leakage in the pixel domain
• Detection of Dipole Modulation in CMB Temperature Anisotropy Maps from WMAP and Planck using Artificial Intelligence
• Estimation of Full Sky Power Spectrum between Intermediate to Large Angular Scales from Partial Sky CMB Anisotropies using Artificial Neural Network

Cited by in corpus (1)

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