CMB-PAInT: An inpainting tool for the cosmic microwave background

The presence of astrophysical emissions in microwave observations forces us to perform component separation to extract the Cosmic Microwave Background (CMB) signal. However, even in the most optimistic cases, there are still strongly contaminated regions, such as the Galactic plane or those with emission from extragalactic point sources, which require the use of a mask. Since many CMB analyses, especially the ones working in harmonic space, need the whole sky map, it is crucial to develop a reliable inpainting algorithm that replaces the values of the excluded pixels by others statistically compatible with the rest of the sky. This is especially important when working with $Q$ and $U$ sky maps in order to obtain $E$- and $B$-mode maps which are free from $E$-to-$B$ leakage. In this work we study a method based on Gaussian Constrained Realizations (GCR), that can deal with both intensity and polarization. Several tests have been performed to asses the validation of the method, including the study of the one-dimensional probability distribution function (1-PDF), E- and B-mode map reconstruction, and power spectra estimation. We have considered two scenarios for the input simulation: one case with only CMB signal and a second one including also Planck PR4 semi-realistic noise. Even if we are limited to low resolution maps, $N_{\mathrm{side}} = $ 64 if $T$, $Q$ and $U$ are considered, we believe that this is a useful approach to be applied to future missions such as LiteBIRD, where the target are the largest scales.