Wavelet reconstruction of E and B modes for CMB polarisation and cosmic shear analyses

TL;DR

This paper introduces wavelet-based methods for accurately separating E and B modes in CMB polarization and cosmic shear data, reducing leakage caused by incomplete sky coverage and improving analysis precision.

Contribution

It develops pseudo and pure wavelet estimators that suppress E-B mixing and ambiguous modes, enhancing mode separation in incomplete sky observations.

Findings

Wavelet estimators outperform harmonic space methods in reducing leakage.

The methods are applicable to CMB polarization and galaxy shear data.

Wavelet-based techniques are computationally efficient and compatible with component separation.

Abstract

We present new methods for mapping the curl-free (E-mode) and divergence-free (B-mode) components of spin 2 signals using spin directional wavelets. Our methods are equally applicable to measurements of the polarisation of the cosmic microwave background (CMB) and the shear of galaxy shapes due to weak gravitational lensing. We derive pseudo and pure wavelet estimators, where E-B mixing arising due to incomplete sky coverage is suppressed in wavelet space using scale- and orientation-dependent masking and weighting schemes. In the case of the pure estimator, ambiguous modes (which have vanishing curl and divergence simultaneously on the incomplete sky) are also cancelled. On simulations, we demonstrate the improvement (i.e., reduction in leakage) provided by our wavelet space estimators over standard harmonic space approaches. Our new methods can be directly interfaced in a coherent and computationally-efficient manner with component separation or feature extraction techniques that also exploit wavelets.