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

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.

32 pages, 25 figures, submitted to MNRAS

References in corpus (2)

• E/B decomposition of finite pixelized CMB maps
• Gabor Transforms on the Sphere with Applications to CMB Power Spectrum Estimation

Cited by in corpus (31)

• Testing the cosmological principle of isotropy: local power spectrum estimates of the WMAP data
• Fast estimation of polarization power spectra using correlation functions
• Myths and Truths Concerning Estimation of Power Spectra
• Power spectrum estimation from high-resolution maps by Gibbs sampling
• Power Asymmetry in Cosmic Microwave Background Fluctuations from Full Sky to Sub-degree Scales: Is the Universe Isotropic?
• Xspect, estimation of the angular power spectrum by computing cross-power spectra with analytical error bars
• CMB temperature and polarisation pseudo-Cl estimators and covariances
• Pseudo-$C_{\ell }$ estimators which do not mix E and B modes
• First Season QUIET Observations: Measurements of CMB Polarization Power Spectra at 43 GHz in the Multipole Range 25 <= ell <= 475
• Second Season QUIET Observations: Measurements of the CMB Polarization Power Spectrum at 95 GHz
• Polarized CMB power spectrum estimation using the pure pseudo-cross-spectrum approach
• Error analysis of quadratic power spectrum estimates for CMB polarization: sampling covariance
• Hybrid Estimation of CMB Polarization Power Spectra
• Probing cosmology with weak lensing selected clusters I: Halo approach and all-sky simulations
• Examining the Effect of the Map-Making Algorithm on Observed Power Asymmetry in WMAP Data
• Separating E and B types of polarization on an incomplete sky
• Performance forecasts for the primordial gravitational wave detection pipelines for AliCPT-1
• QuickPol: Fast calculation of effective beam matrices for CMB polarization
• Cosmological parameters and the WMAP data revisited
• Efficiency of pseudo-spectrum methods for estimation of Cosmic Microwave Background B-mode power spectrum
• Pure pseudo-C_l estimators for CMB B-modes
• Fast and precise map-making for massively multi-detector CMB experiments
• Probing the statistical properties of CMB $B$-mode polarization through Minkowski Functionals
• Preferred axis of CMB parity asymmetry in the masked maps
• Data analysis methods for the cosmic microwave background
• Euclid: Covariance of weak lensing pseudo-$C_{\ell }$ estimates. Calculation, comparison to simulations, and dependence on survey geometry
• Scalar quadratic maximum likelihood estimators for the CMB cross power spectrum
• Fast scalar quadratic maximum likelihood estimators for the CMB B-mode power spectrum
• A comprehensive study of Modulation effects on CMB Polarization
• On the linear filters for point source extraction of the Planck mission
• A Search for X-Ray Reionization Signatures from Cross-Correlation of Wmap and ROSAT Rass Data