Pure E and B polarization maps via Wiener filtering

TL;DR

This paper presents a Wiener filtering approach to efficiently produce pure E and B polarization maps from CMB data, improving upon traditional methods by incorporating noise and other contaminants.

Contribution

It introduces a novel perspective of using Wiener filtering for pure E and B map construction, enabling more efficient and generalized separation techniques.

Findings

Wiener filtering can produce pure polarization maps efficiently.

The method accounts for noise and contaminants in the data.

Generalizations include correlations with temperature anisotropy.

Abstract

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.