Efficient Wiener filtering without preconditioning
  We present a new approach to calculate the Wiener filter solution of general
data sets. It is trivial to implement, flexible, numerically absolutely stable,
and guaranteed to converge. Most importantly, it does not require an ingenious
choice of preconditioner to work well. The method is capable of taking into
account inhomogeneous noise distributions and arbitrary mask geometries. It
iteratively builds up the signal reconstruction by means of a messenger field,
introduced to mediate between the different preferred bases in which signal and
noise properties can be specified most conveniently. Using cosmic microwave
background (CMB) radiation data as a showcase, we demonstrate the capabilities
of our scheme by computing Wiener filtered WMAP7 temperature and polarization
maps at full resolution for the first time. We show how the algorithm can be
modified to synthesize fluctuation maps, which, combined with the Wiener filter
solution, result in unbiased constrained signal realizations, consistent with
the observations. The algorithm performs well even on simulated CMB maps with
Planck resolution and dynamic range.
