Optimal and fast E/B separation with a dual messenger field
  We adapt our recently proposed dual messenger algorithm for spin field
reconstruction and showcase its efficiency and effectiveness in Wiener
filtering polarized cosmic microwave background (CMB) maps. Unlike conventional
preconditioned conjugate gradient (PCG) solvers, our preconditioner-free
technique can deal with high-resolution joint temperature and polarization maps
with inhomogeneous noise distributions and arbitrary mask geometries with
relative ease. Various convergence diagnostics illustrate the high quality of
the dual messenger reconstruction. In contrast, the PCG implementation fails to
converge to a reasonable solution for the specific problem considered. The
implementation of the dual messenger method is straightforward and guarantees
numerical stability and convergence. We show how the algorithm can be modified
to generate fluctuation maps, which, combined with the Wiener filter solution,
yield unbiased constrained signal realizations, consistent with observed data.
This algorithm presents a pathway to exact global analyses of high-resolution
and high-sensitivity CMB data for a statistically optimal separation of E and B
modes. It is therefore relevant for current and next-generation CMB
experiments, in the quest for the elusive primordial B-mode signal.
