Pure E and B polarization maps via Wiener filtering

Abstract

In order to draw scientific conclusions from observations of cosmic microwave background (CMB) polarization, it is necessary to separate the contributions of the E and B components of the data. For data with incomplete sky coverage, there are ambiguous modes, which can be sourced by either E or B signals. Techniques exist for producing "pure" E and B maps, which are guaranteed to be free of cross-contamination, although the standard method, which involves constructing an eigenbasis, has a high computational cost. We show that such pure maps can be thought of as resulting from the application of a Wiener filter to the data. This perspective leads to far more efficient methods of producing pure maps. Moreover, by expressing the idea of purification in the general framework of Wiener filtering (i.e., maximization of a posterior probability), it leads to a variety of generalizations of the notion of pure E and B maps, e.g., accounting for noise or other contaminants in the data as well as correlations with temperature anisotropy.

Modified to include demonstrations of the method on the spherical sky. Matches version accepted for publication in Phys. Rev. D

References in corpus (12)

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• 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
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• Estimation of Polarized Power Spectra by Gibbs sampling
• Efficient Wiener filtering without preconditioning
• CMB E/B decomposition of incomplete sky: a pixel space approach
• Efficient decomposition of cosmic microwave background polarization maps into pure E, pure B, and ambiguous components
• Wiener filter reloaded: fast signal reconstruction without preconditioning
• Wavelet reconstruction of E and B modes for CMB polarisation and cosmic shear analyses
• Spin-SILC: CMB polarisation component separation with spin wavelets

Cited by in corpus (12)

• Planck 2018 results. VII. Isotropy and Statistics of the CMB
• Methods for pixel domain correction of EB leakage
• Wiener filter reloaded: fast signal reconstruction without preconditioning
• Fingerprinting the effects of hyperfine structure on CH and OH far infrared spectra using Wiener filter deconvolution
• Wiener filtering and pure E/B decomposition of CMB maps with anisotropic correlated noise
• Fingerprint of Galactic Loop I on polarized microwave foregrounds
• Optimal and fast E/B separation with a dual messenger field
• Fast scalar quadratic maximum likelihood estimators for the CMB B-mode power spectrum
• Statistical imprints of CMB B-type polarization leakage in an incomplete sky survey analysis
• Testing Quadratic Maximum Likelihood estimators for forthcoming Stage-IV weak lensing surveys
• From top-hat masking to smooth transitions: P-filter and its application to polarized microwave sky maps
• Reconstruction of full sky CMB $\mathbf{E}$ and $\mathbf{B}$ modes spectra removing $\mathbf{E}$-to-$\mathbf{B}$ leakage from partial sky using deep learning