Efficient Wiener filtering without preconditioning

TL;DR

This paper introduces a new, stable, and easy-to-implement Wiener filtering method that handles complex noise and mask geometries without preconditioning, demonstrated on cosmic microwave background data.

Contribution

The authors develop a preconditioner-free Wiener filtering algorithm using a messenger field, capable of handling inhomogeneous noise and arbitrary masks, with demonstrated application to CMB data.

Findings

Successfully computed full-resolution Wiener filtered WMAP7 maps.

Capable of synthesizing unbiased constrained signal realizations.

Performs efficiently on simulated Planck-resolution CMB maps.

Abstract

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.