Pure E and B polarization maps via Wiener filtering
  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.
