Mixed Needlets

TL;DR

This paper introduces mixed needlets, a new type of wavelet system on spin line bundles over the sphere, using standard spherical harmonics, with detailed analysis of their mathematical properties and potential astrophysical applications.

Contribution

It proposes mixed needlets based on usual spherical harmonics, offering an alternative to existing spin needlet constructions, and thoroughly investigates their mathematical properties.

Findings

Mixed needlets form an exact tight frame.

They exhibit localization and asymptotic uncorrelation.

Applicable to astrophysical data analysis.

Abstract

The construction of needlet-type wavelets on sections of the spin line bundles over the sphere has been recently addressed in Geller and Marinucci (2008), and Geller et al. (2008,2009). Here we focus on an alternative proposal for needlets on this spin line bundle, in which needlet coefficients arise from the usual, rather than the spin, spherical harmonics, as in the previous constructions. We label this system mixed needlets and investigate in full their properties, including localization, the exact tight frame characterization, reconstruction formula, decomposition of functional spaces, and asymptotic uncorrelation in the stochastic case. We outline astrophysical applications.