Wiener filter reloaded: fast signal reconstruction without
  preconditioning
  We present a high performance solution to the Wiener filtering problem via a
formulation that is dual to the recently developed messenger technique. This
new dual messenger algorithm, like its predecessor, efficiently calculates the
Wiener filter solution of large and complex data sets without preconditioning
and can account for inhomogeneous noise distributions and arbitrary mask
geometries. We demonstrate the capabilities of this scheme in signal
reconstruction by applying it on a simulated cosmic microwave background (CMB)
temperature data set. The performance of this new method is compared to that of
the standard messenger algorithm and the preconditioned conjugate gradient
(PCG) approach, using a series of well-known convergence diagnostics and their
processing times, for the particular problem under consideration. This variant
of the messenger algorithm matches the performance of the PCG method in terms
of the effectiveness of reconstruction of the input angular power spectrum and
converges smoothly to the final solution. The dual messenger algorithm
outperforms the standard messenger and PCG methods in terms of execution time,
as it runs to completion around 2 and 3-4 times faster than the respective
methods, for the specific problem considered.
