CMB power spectrum estimation using wavelets

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 nonstationary uncorrelated noise 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 nonstationary noise. In the case of a single experiment, we compare this method with pseudo-C_ℓ methods. The performance of the needlet spectral estimators (NSE) compares very favorably to the best pseudo-C_ℓ 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 wideband error bar is highlighted. The needlet spectral estimator is a powerful, tunable tool which is very well suited to the angular power spectrum estimation of spherical data such as incomplete and noisy CMB maps.