A Global ILC Approach in Pixel Space over Large Angular Scales of the Sky using CMB Covariance Matrix

We propose a new internal linear combination (ILC) method in the pixel space, applicable on large angular scales of the sky, to estimate a foreground minimized Cosmic Microwave Background (CMB) temperature anisotropy map by incorporating prior knowledge about the theoretical CMB covariance matrix. Usual ILC method in pixel space, on the contrary, does not use any information about the underlying CMB covariance matrix. The new approach complements the usual pixel space ILC technique specifically at low multipole region, using global information available from theoretical CMB covariance matrix as well as from the data. Since we apply our method over the large scale on the sky containing low multipoles we perform foreground minimization globally. We apply our methods on low resolution Planck and WMAP foreground contaminated CMB maps and validate the methodology by performing detailed Monte-Carlo simulations. Our cleaned CMB map and its power spectrum have significantly less error than those obtained following usual ILC technique at low resolution that does not use CMB covariance information. Another very important advantage of our method is that the cleaned power spectrum does not have any negative bias at the low multipoles because of effective suppression of CMB-foreground chance correlations on large angular scales of the sky. Our cleaned CMB map and its power spectrum match well with those estimated by other research groups.