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Fast CMB Power Spectrum Estimation of Temperature and Polarisation with Gabor Transforms

Frode K. Hansen·Krzysztof M. Gorski
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Abstract

We extend the analysis of Gabor transforms on a Cosmic Microwave Background (CMB) temperature map (Hansen, Gorski and Hivon 2002) to polarisation. We study the temperature and polarisation power spectra on the cut sky, the so-called pseudo power spectra. The transformation kernels relating the full-sky polarisation power spectra and the polarisation pseudo power spectra are found to be similar to the kernel for the temperature power spectrum. This fact is used to construct a fast power spectrum estimation algorithm using the pseudo power spectrum of temperature and polarisation as data vectors in a maximum likelihood approach. Using the pseudo power spectra as input to the likelihood analysis solves the problem of having to invert huge matrices which makes the standard likelihood approach infeasible.

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Frode K. Hansen, Krzysztof M. Gorski. 2002-07-24. Fast CMB Power Spectrum Estimation of Temperature and Polarisation with Gabor Transforms. https://doi.org/10.1046/j.1365-8711.2003.06695.x

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