Spin Wavelets on the Sphere

TL;DR

This paper extends wavelet analysis on the sphere to spin fields, introducing needlet-type spin wavelets with applications to cosmology, especially for analyzing Cosmic Microwave Background polarization data.

Contribution

It generalizes needlet wavelets to sections of line bundles on the sphere, enabling analysis of spin functions with localization and stochastic properties.

Findings

Introduces needlet-type spin wavelets for line bundle sections.

Analyzes localization in real and harmonic domains.

Investigates stochastic properties for spin random fields.

Abstract

In recent years, a rapidly growing literature has focussed on the construction of wavelet systems to analyze functions defined on the sphere. Our purpose in this paper is to generalize these constructions to situations where sections of line bundles, rather than ordinary scalar-valued functions, are considered. In particular, we propose {\em needlet-type spin wavelets} as an extension of the needlet approach recently introduced by Narcowich, Petrushev and Ward, and then considered for more general manifolds by Geller and Mayeli. We discuss localization properties in the real and harmonic domains, and investigate stochastic properties for the analysis of spin random fields. Our results are strongly motivated by cosmological applications, in particular in connection to the analysis of Cosmic Microwave Background polarization data.