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Incomplete sky analysis of cosmic microwave background (CMB) polarizationspectra poses a major problem of leakage between $E$- and $B$-modes. We presenta machine learning approach to remove this $E$-to-$B$ leakage using aconvolutional neural network (CNN) in presence of detector noise. The CNNpredicts the full sky $E$- and $B$-modes spectra for multipoles $2 \leq \ell\leq 384$ from the partial sky spectra for $N_{\rm{side}} = 256$. We usetensor-to-scalar ratio $r=0.001$ to simulate the CMB polarization maps. Wetrain our CNN using $10^5$ full sky target spectra and an equal number of noisecontaminated partial sky spectra obtained from the simulated maps. The CNNworks well for two masks covering the sky area of $\sim 80\%$ and $\sim 10\%$respectively after training separately for each mask. For the assumedtheoretical $E$- and $B$-modes spectra, predicted full sky $E$- and $B$-modesspectra agree well with the corresponding target spectra and their means agreewith theoretical spectra. The CNN preserves the cosmic variances at eachmultipole, effectively removes correlations of the partial sky $E$- and$B$-modes spectra, and retains the entire statistical properties of the targetsavoiding the problem of so-called $E$-to-$B$ leakage for the chosen theoreticalmodel.

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