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

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

2002-07-24

arxiv.org/abs/astro-ph/0207526v1

Mon.Not.Roy.Astron.Soc.343:559,2003

Astronomy and Astrophysics

Astrophysics

32 pages, 25 figures, submitted to MNRAS

Scientific paper

10.1046/j.1365-8711.2003.06695.x

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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