Spin Needlets for Cosmic Microwave Background Polarization Data Analysis

TL;DR

This paper introduces spin needlets, a new wavelet tool for analyzing CMB polarization data, enabling localized, uncorrelated analysis of spin 2 fields and facilitating statistical tests and map reconstructions.

Contribution

The paper adapts spin needlets for CMB polarization analysis, demonstrating their properties and applications in power spectrum estimation, non-Gaussianity testing, and E/B map reconstruction.

Findings

Spin needlets are localized in pixel and harmonic space.

They exhibit asymptotic uncorrelation for statistical analysis.

Applications include power spectrum relation, non-Gaussianity tests, and E/B map reconstruction.

Abstract

Scalar wavelets have been used extensively in the analysis of Cosmic Microwave Background (CMB) temperature maps. Spin needlets are a new form of (spin) wavelets which were introduced in the mathematical literature by Geller and Marinucci (2008) as a tool for the analysis of spin random fields. Here we adopt the spin needlet approach for the analysis of CMB polarization measurements. The outcome of experiments measuring the polarization of the CMB are maps of the Stokes Q and U parameters which are spin 2 quantities. Here we discuss how to transform these spin 2 maps into spin 2 needlet coefficients and outline briefly how these coefficients can be used in the analysis of CMB polarization data. We review the most important properties of spin needlets, such as localization in pixel and harmonic space and asymptotic uncorrelation. We discuss several statistical applications, including the relation of angular power spectra to the needlet coefficients, testing for non-Gaussianity on polarization data, and reconstruction of the E and B scalar maps.