Polarized wavelets and curvelets on the sphere
arXiv:0902.0574 · doi:10.1051/0004-6361/200811343
Abstract
The statistics of the temperature anisotropies in the primordial cosmic microwave background radiation field provide a wealth of information for cosmology and for estimating cosmological parameters. An even more acute inference should stem from the study of maps of the polarization state of the CMB radiation. Measuring the extremely weak CMB polarization signal requires very sensitive instruments. The full-sky maps of both temperature and polarization anisotropies of the CMB to be delivered by the upcoming Planck Surveyor satellite experiment are hence being awaited with excitement. Multiscale methods, such as isotropic wavelets, steerable wavelets, or curvelets, have been proposed in the past to analyze the CMB temperature map. In this paper, we contribute to enlarging the set of available transforms for polarized data on the sphere. We describe a set of new multiscale decompositions for polarized data on the sphere, including decimated and undecimated Q-U or E-B wavelet transforms and Q-U or E-B curvelets. The proposed transforms are invertible and so allow for applications in data restoration and denoising.
Accepted. Full paper will figures available at http://jstarck.free.fr/aa08_pola.pdf
References in corpus (23)
- HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
- An All-Sky Analysis of Polarization in the Microwave Background
- Detection of Polarization in the Cosmic Microwave Background using DASI
- Detection of non-Gaussianity in the WMAP 1-year data using spherical wavelets
- Spherical Needlets for CMB Data Analysis
- Wavelets, ridgelets and curvelets on the sphere
- E/B decomposition of finite pixelized CMB maps
- Exact reconstruction with directional wavelets on the sphere
- Wavelet analysis and the detection of non-Gaussianity in the CMB
- CMB Polarization Experiments
- SZ and CMB reconstruction using Generalized Morphological Component Analysis
- Applications of Wavelets to the Analysis of Cosmic Microwave Background Maps
- Cosmological applications of a wavelet analysis on the sphere
- Spherical Mexican Hat wavelet: an application to detect non-Gaussianity in the COBE-DMR maps
- CMB data analysis and sparsity
- CMB power spectrum estimation using wavelets
- Detection and discrimination of cosmological non-Gaussian signatures by multi-scale methods
- Fast spin +-2 spherical harmonics transforms and application in cosmology
- Cosmological non-Gaussian Signature Detection: Comparing Performance of Different Statistical Tests
- Blind component separation in wavelet space. Application to CMB analysis
- Statistics of phase correlations as a test for non-Gaussianity of the CMB maps
- Non-Random Phases in Non-Trivial Topologies
- Steerable wavelet analysis of CMB structures alignment
Cited by in corpus (12)
- S2LET: A code to perform fast wavelet analysis on the sphere
- Localisation of directional scale-discretised wavelets on the sphere
- Spherical 3D Isotropic Wavelets
- Directional spin wavelets on the sphere
- Wavelet-Bayesian inference of cosmic strings embedded in the cosmic microwave background
- SILC: a new Planck Internal Linear Combination CMB temperature map using directional wavelets
- A Simple Proposal for Radial 3D Needlets
- Needatool: A Needlet Analysis Tool for Cosmological Data Processing
- Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs
- Directional wavelets on -dimensional spheres
- Polarized CMB recovery with sparse component separation
- Learning sparse representations on the sphere