Polarized wavelets and curvelets on the sphere

TL;DR

This paper introduces new multiscale transform methods, including wavelets and curvelets, for analyzing polarized data on the sphere, enhancing tools for cosmic microwave background studies.

Contribution

It presents novel invertible multiscale decompositions for polarized spherical data, expanding analysis options for CMB polarization maps.

Findings

Developed decimated and undecimated Q-U/E-B wavelet transforms

Created Q-U/E-B curvelet transforms for polarized data

Transforms are invertible, enabling data restoration and denoising

Abstract

The statistics of the temperature anisotropies in the primordial cosmic microwave background radiation field provide a wealth of information for cosmology and for estimating cosmological parameters. An even more acute inference should stem from the study of maps of the polarization state of the CMB radiation. Measuring the extremely weak CMB polarization signal requires very sensitive instruments. The full-sky maps of both temperature and polarization anisotropies of the CMB to be delivered by the upcoming Planck Surveyor satellite experiment are hence being awaited with excitement. Multiscale methods, such as isotropic wavelets, steerable wavelets, or curvelets, have been proposed in the past to analyze the CMB temperature map. In this paper, we contribute to enlarging the set of available transforms for polarized data on the sphere. We describe a set of new multiscale decompositions for polarized data on the sphere, including decimated and undecimated Q-U or E-B wavelet transforms and Q-U or E-B curvelets. The proposed transforms are invertible and so allow for applications in data restoration and denoising.