Nearly tight frames of spin wavelets on the sphere

TL;DR

This paper demonstrates that spin wavelets on the sphere can be constructed as nearly tight frames, facilitating analysis of cosmic microwave background polarization with localized frame elements.

Contribution

It introduces a method to form nearly tight frames of spin wavelets on the sphere, improving their applicability in astrophysical data analysis.

Findings

Spin wavelets can form nearly tight frames on the sphere.

Frame elements are localized within geodesic balls.

Application to polarization analysis of cosmic microwave background.

Abstract

We show that the spin wavelets on the sphere $S^2$, which were constructed by the first author and Marinucci in an earlier article, can be chosen so as to form a nearly tight frame. These spin wavelets can be applied to the study of the polarization of cosmic microwave background radiation. For certain of these frames, there is a positive $C$ such that each frame element at scale $a^j$ is supported in a geodesic ball of radius $Ca^j$.