CMB power spectrum estimation using wavelets

TL;DR

This paper introduces a needlet-based spectral estimation method for the CMB power spectrum, effectively handling non-stationarity, foregrounds, and multiple experiments, outperforming traditional Pseudo-$C_ll$ methods in simulations.

Contribution

The paper presents a novel needlet (wavelet) approach for spectral estimation on the sphere, improving accuracy and versatility over existing methods for incomplete and noisy CMB data.

Findings

Needlet estimators outperform Pseudo-$C_ll$ methods in simulations.

The method effectively combines data from multiple experiments.

It provides a single wide-band error bar for the power spectrum.

Abstract

Observations of the Cosmic Microwave Background (CMB) provide increasingly accurate information about the structure of the Universe at the recombination epoch. Most of this information is encoded in the angular power spectrum of the CMB. The aim of this work is to propose a versatile and powerful method for spectral estimation on the sphere which can easily deal with non-stationarity, foregrounds and multiple experiments with various specifications. In this paper, we use needlets (wavelets) on the sphere to construct natural and efficient spectral estimators for partially observed and beamed CMB with non stationary noise. In the case of a single experiment, we compare this method with Pseudo-$C_\ell$ methods. The performance of the needlet spectral estimators (NSE) compares very favorably to the best Pseudo--$C_\ell$ estimators, over the whole multipole range. On simulations with a simple model (CMB + uncorrelated noise with known variance per pixel + mask), they perform uniformly better. Their distinctive ability to aggregate many different experiments, to control the propagation of errors and to produce a single wide-band error bars is highlighted. The needlet spectral estimator is a powerful, tunable tool which is very well suited to angular power spectrum estimation of spherical data such as incomplete and noisy CMB maps.