Title: Preconditioner-free Wiener filtering with a dense noise matrix,
Abstract: This work extends the Elsner & Wandelt (2013) iterative method for efficient,
preconditioner-free Wiener filtering to cases in which the noise covariance
matrix is dense, but can be decomposed into a sum whose parts are sparse in
convenient bases. The new method, which uses multiple messenger fields,
reproduces Wiener filter solutions for test problems, and we apply it to a case
beyond the reach of the Elsner & Wandelt (2013) method. We compute the Wiener
filter solution for a simulated Cosmic Microwave Background map that contains
spatially-varying, uncorrelated noise, isotropic $1/f$ noise, and large-scale
horizontal stripes (like those caused by the atmospheric noise). We discuss
simple extensions that can filter contaminated modes or inverse-noise filter
the data. These techniques help to address complications in the noise
properties of maps from current and future generations of ground-based
Microwave Background experiments, like Advanced ACTPol, Simons Observatory, and
CMB-S4.