Global-NILC: a bias reduction effort for NILC at large angular scale*

The detection of the polarization induced by the primordial gravitational wave (B-mode) in the Cosmic Microwave Background (CMB) is the primary focus for future CMB projects. However, the polarized Galactic foreground overwhelms the primordial polarization signature from the CMB at all frequencies, prompting the need for reliable component separation methods. The needlet internal linear combination method (NILC) is a blind component separation method constructed in the spherical wavelet (needlet) domain. NILC removes the Galactic foreground from the CMB signal using map-space variance minimization. The method is an internal linear combination (ILC) variant developed for the Wilkinson Microwave Anistropy Probe (WMAP) and later extensively used for analyzing data from the Planck mission. While NILC yields highly accurate results at small angular scale, the science of CMB concerns the large scale measurement of B-mode polarization. This project aim to improve the bias level for NILC at large angular scale. We applied our NILC variant to low-resolution maps. Our approach computes the theoretical CMB covariance matrices for each needlet window in the pixel space. We incorporate these covariance matrices into the ILC weight computation, taking information from both the theoretical CMB model and actual data into account. We assess our method with Monte Carlo simulations. Simulation results show clear progress reducing the bias level for NILC at large angular scales under different needlet decomposition schemes.