Efficiency of pseudo-spectrum methods for estimation of Cosmic Microwave
  Background B-mode power spectrum
  Estimation of the B-mode angular power spectrum of polarized anisotropies of
the cosmic microwave background (CMB) is a key step towards a full exploitation
of the scientific potential of this probe. In the context of pseudo-spectrum
methods the major challenge is related to a contamination of the B-mode
spectrum estimate with residual power of much larger E-mode. This so-called
E-to-B leakage is unavoidably present whenever an incomplete sky map is only
available, as is the case for any realistic observation. The leakage has to be
then minimized or removed and ideally in such a way that neither a bias nor
extra variance is introduced. In this paper, we compare from these two
perspectives three different methods proposed recently in this context Refs.
Smith 2006, Zhao & Baskaran 2010, Kim & Naselsky 2010, which we first introduce
within a common algebraic framework of the so-called chi-fields and then study
their performance on two different experimental configurations - one
corresponding to a small-scale experiment covering 1% of the sky motivated by
current ground-based or balloon-borne experiments and another - to a nearly
full-sky experiment, e.g., a possible CMB B-mode satellite mission. We find
that though all these methods allow to reduce significantly the level of the
E-to-B leakage, it is the method of Smith 2006, which at the same time ensures
the smallest error bars in all experimental configurations studied here, owing
to the fact that it permits straightforwardly for an optimization of the sky
apodization of the polarization maps used for the estimation. For a
satellite-like experiment, this method enables a detection of B-mode power
spectrum at large angular scales but only after appropriate binning. The method
of Zhao & Baskaran 2010 is a close runner-up in the case of a nearly full sky
coverage.
