In order to draw scientific conclusions from observations of cosmic microwave background (CMB) polarization, it is necessary to separate the contributions of the E and B components of the data. For data with incomplete sky coverage, there are ambiguous modes, which can be sourced by either E or B signals. Techniques exist for producing "pure" E and B maps, which are guaranteed to be free of cross-contamination, although the standard method, which involves constructing an eigenbasis, has a high computational cost. We show that such pure maps can be thought of as resulting from the application of a Wiener filter to the data. This perspective leads to far more efficient methods of producing pure maps. Moreover, by expressing the idea of purification in the general framework of Wiener filtering (i.e., maximization of a posterior probability), it leads to a variety of generalizations of the notion of pure E and B maps, e.g., accounting for noise or other contaminants in the data as well as correlations with temperature anisotropy.
Physical Review D
- Pub Date:
- August 2017
- Astrophysics - Cosmology and Nongalactic Astrophysics
- Modified to include demonstrations of the method on the spherical sky. Matches version accepted for publication in Phys. Rev. D