Needlets and foreground removal for SKAO hydrogen intensity maps

Intensity Mapping (IM) of the 21-cm line of the neutral hydrogen (\textsc{Hi}) has become a compelling new technique to map the large-scale structure of the Universe. One of the main challenges is the presence of strong foreground emissions of several orders of magnitude larger than the \textsc{Hi}~signal. Here, we implement a version of the Principal Component Analysis, a blind component-separation technique, based on a kind of spherical wavelets called needlets. These functions exploit double localization both in real and in harmonic space. We test Need-PCA performances on a set of maps that simulates the SKA MID radio telescope in the AA4 configuration. We compare our results with other component separation methods such as Generalised Morphological Component Analysis (GMCA) and Generalized Needlet Internal Linear Combination (GNILC). All the methods have comparable results, recovering the \textsc{Hi}~signal within 10\% accuracy across the frequency channels, in the multipole range 30 $\lesssim \ell \lesssim$ 136. We also test our pipeline in the presence of systematics such as polarization leakage. We find that the cleaning methods are insensitive to the presence of such systematic, yielding the same results as in the leakage-free case. Finally, under the assumption of a realistic telescope beam with sidelobes, we find that standard PCA and GMCA fails to recover the \textsc{Hi}~signal at larger scales, while the Need-PCA and Need-GMCA are less affected. GNILC tends to over-clean, yielding to a loss of the signal.