Using needlets to estimate the power spectrum

Abstract

The statistical analysis of the Cosmic Microwave Background radiation to make estimates of the Power Spectrum is a comutationally heavy operation, involving large covariance matrices.

In this thesis I explore the possibility of using Needlet Transformations on the CMB signal to make the covariance matrix simpler. Needlet transformations are wavelets designed to work on spherical fields, and has properties that can potentially simplify the covariance matrix. The results of this thesis indicate that the conditions where needlet transformations actually provide simple matrices are not met. The use of needlet transformation to estimate the power spectrum is not viable with the algorithm tested.