Multi-resolution Bayesian CMB component separation through
  Wiener-filtering with a pseudo-inverse preconditioner
  We present a Bayesian model for multi-resolution CMB component separation
based on Wiener filtering and/or computation of constrained realizations,
extending a previously developed framework. We also develop an efficient solver
for the corresponding linear system for the associated signal amplitudes. The
core of this new solver is an efficient preconditioner based on the
pseudo-inverse of the coefficient matrix of the linear system. In the full sky
coverage case, the method gives a speed-up of 2--3x in compute time compared to
a simple diagonal preconditioner, and it is easier to implement in terms of
practical computer code. In the case where a mask is applied and prior-driven
constrained realization is sought within the mask, this is the first time full
convergence has been achieved at the full resolution of the Planck dataset.
Prototype benchmark code is available at https://github.com/dagss/cmbcr .
