Towards efficient and optimal analysis of CMB anisotropies on a masked sky

TL;DR

This paper develops a computationally efficient estimator for analyzing CMB anisotropies on masked skies, nearly matching the optimal maximum likelihood method's performance despite foreground masking.

Contribution

It introduces an augmented basis for estimators that accounts for mode coupling caused by masking, improving analysis efficiency and accuracy.

Findings

Achieves near-optimal results with realistic masks

Reduces information loss compared to pseudo-C_l methods

Validates methodology with WMAP-like data

Abstract

Strong foreground contamination in high resolution CMB data requires masking which introduces statistical anisotropies and renders a full maximum likelihood analysis numerically intractable. Standard analysis methods like the pseudo-C_l framework lead to information loss due to estimator suboptimalities. We set out and validate a methodology for numerically efficient estimators for a masked sky that recover nearly as much information as a full maximum likelihood procedure. In addition to the standard pseudo-C_l statistic, the approach introduces an augmented basis designed to account for the mode coupling due to the masking of the sky. We motivate the choice of this basis by describing the basic structure of the covariance matrix. We demonstrate that the augmented estimator can achieve near-optimal results in the presence of a WMAP-realistic mask.