Optimal and fast E/B separation with a dual messenger field

TL;DR

This paper introduces a dual messenger algorithm for efficient, stable E/B mode separation in polarized CMB maps, outperforming traditional methods in high-resolution, inhomogeneous noise, and complex mask scenarios, aiding primordial B-mode detection.

Contribution

The paper adapts and demonstrates a preconditioner-free dual messenger algorithm for fast, stable E/B separation in CMB data, suitable for high-resolution, complex noise, and mask conditions.

Findings

The dual messenger method converges rapidly and reliably.

It outperforms PCG solvers in challenging scenarios.

It enables unbiased constrained signal realizations.

Abstract

We adapt our recently proposed dual messenger algorithm for spin field reconstruction and showcase its efficiency and effectiveness in Wiener filtering polarized cosmic microwave background (CMB) maps. Unlike conventional preconditioned conjugate gradient (PCG) solvers, our preconditioner-free technique can deal with high-resolution joint temperature and polarization maps with inhomogeneous noise distributions and arbitrary mask geometries with relative ease. Various convergence diagnostics illustrate the high quality of the dual messenger reconstruction. In contrast, the PCG implementation fails to converge to a reasonable solution for the specific problem considered. The implementation of the dual messenger method is straightforward and guarantees numerical stability and convergence. We show how the algorithm can be modified to generate fluctuation maps, which, combined with the Wiener filter solution, yield unbiased constrained signal realizations, consistent with observed data. This algorithm presents a pathway to exact global analyses of high-resolution and high-sensitivity CMB data for a statistically optimal separation of E and B modes. It is therefore relevant for current and next-generation CMB experiments, in the quest for the elusive primordial B-mode signal.