Spherical Needlets for CMB Data Analysis
arXiv:0707.0844 · doi:10.1111/j.1365-2966.2007.12550.x
Abstract
We discuss Spherical Needlets and their properties. Needlets are a form of spherical wavelets which do not rely on any kind of tangent plane approximation and enjoy good localization properties in both pixel and harmonic space; moreover needlets coefficients are asymptotically uncorrelated at any fixed angular distance, which makes their use in statistical procedures very promising. In view of these properties, we believe needlets may turn out to be especially useful in the analysis of Cosmic Microwave Background (CMB) data on the incomplete sky, as well as of other cosmological observations. As a final advantage, we stress that the implementation of needlets is computationally very convenient and may rely completely on standard data analysis packages such as HEALPix.
7 pages, 7 figures
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- Needlet Detection of Features in WMAP CMB Sky and the Impact on Anisotropies and Hemispherical Asymmetries
- The needlets bispectrum
- Statistical challenges in the analysis of Cosmic Microwave Background radiation
- Polarized wavelets and curvelets on the sphere
- Spin Needlets for Cosmic Microwave Background Polarization Data Analysis
- Asymptotic Uncorrelation for Mexican Needlets
- Nearly Tight Frames and Space-Frequency Analysis on Compact Manifolds