On spin scale-discretised wavelets on the sphere for the analysis of CMB polarisation

TL;DR

This paper introduces a novel spin wavelet transform on the sphere for analyzing CMB polarization, enabling directional analysis of spin signals and improved recovery of E- and B-modes from incomplete sky data.

Contribution

It extends scalar wavelet transforms to arbitrary spin signals on the sphere, providing a new tool for CMB polarization analysis.

Findings

Effective recovery of E- and B-modes from partial-sky data

Extension of wavelet transform to arbitrary spin signals

Enhanced directional analysis of CMB polarization

Abstract

A new spin wavelet transform on the sphere is proposed to analyse the polarisation of the cosmic microwave background (CMB), a spin $\pm 2$ signal observed on the celestial sphere. The scalar directional scale-discretised wavelet transform on the sphere is extended to analyse signals of arbitrary spin. The resulting spin scale-discretised wavelet transform probes the directional intensity of spin signals. A procedure is presented using this new spin wavelet transform to recover E- and B-mode signals from partial-sky observations of CMB polarisation.