Open AccessFast cosmic microwave background power spectrum estimation of temperature and polarization with Gabor transforms
Author(s) -
Hansen Frode K.,
Górski Krzysztof M.
Publication year - 2003
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2003.06695.x
Subject(s) - cosmic microwave background , physics , polarization (electrochemistry) , spectral density , spectral line , astrophysics , computational physics , sky , microwave , optics , statistics , astronomy , mathematics , quantum mechanics , chemistry , anisotropy
We extend the analysis of Gabor transforms on a cosmic microwave background temperature map to polarization. We study the temperature and polarization power spectra on the cut sky, the so‐called pseudo‐power spectra. The transformation kernels relating the full‐sky polarization power spectra and the polarization 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 polarization 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.