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Filling in CMB map missing data using constrained Gaussian realizations

M. Bucher,T. Louis

Published 2011 in arXiv: Cosmology and Nongalactic Astrophysics

ABSTRACT

For analyzing maps of the cosmic microwave background sky, it is necessary to mask out the region around the Galactic equator where the parasitic foreground emission is strongest as well as the brightest compact sources. Since many of the analyses of the data, particularly those searching for non-Gaussianity of a primordial origin, are most straightforwardly carried out on full-sky maps, it is of great interest to develop ecient algorithms for lling in the missing information in a plausible way. In this paper we explore algorithms for lling in based on constrained Gaussian realizations. Although carrying out such realizations is in principle straightforward, for nely pixelized maps as will be required for the Planck analysis a direct brute force method is not numerically tractable. Here we present some concrete solutions to this problem, both on a spatially at sky with periodic boundary conditions and on the pixelized sphere. One approach is to solve the linear system with an appropriately preconditioned conjugate gradient method. While this approach was successfully implemented on a rectangular domain with periodic boundary conditions and worked even for very wide masked regions, we found that the method failed on the pixelized sphere for reasons that we explain here. We present an approach that works for full-sky pixelized maps on the sphere involving a kernel-based multi-resolution Laplace solver followed by a series of conjugate gradient corrections near the boundary of the mask.

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