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arXiv 0811.2881astro-ph
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用于宇宙微波背景极化数据分析的自旋针

Spin Needlets for Cosmic Microwave Background Polarization Data Analysis

Daryl Geller, Frode K. Hansen, Domenico Marinucci, Gerard Kerkyacharian, Dominique Picard

摘要:

标量小波在宇宙微波背景(CMB)温度图分析中得到了广泛的应用。自旋针状波是一种新形式的(自旋)小波,由Geller和Marinucci(2008)在数学文献中引入,作为分析自旋随机场的工具。在这里,我们采用自旋针的方法来分析CMB偏振测量。测量CMB偏振的实验结果是斯托克斯Q和U参数的映射,它们是自旋2量。在这里,我们讨论如何将这些自旋2映射到自旋2针状系数,并简要概述这些系数可以用于分析CMB偏振数据。我们回顾了自旋针状体最重要的性质,如在像素和调和空间中的局部化和渐近不相关性。我们讨论了几个统计应用,包括角功率谱的针状系数的关系,测试非高斯偏振数据,和重建的E和B标量地图。

英文摘要:

Scalar wavelets have been used extensively in the analysis of Cosmic Microwave Background (CMB) temperature maps. Spin needlets are a new form of (spin) wavelets which were introduced in the mathematical literature by Geller and Marinucci (2008) as a tool for the analysis of spin random fields. Here we adopt the spin needlet approach for the analysis of CMB polarization measurements. The outcome of experiments measuring the polarization of the CMB are maps of the Stokes Q and U parameters which are spin 2 quantities. Here we discuss how to transform these spin 2 maps into spin 2 needlet coefficients and outline briefly how these coefficients can be used in the analysis of CMB polarization data. We review the most important properties of spin needlets, such as localization in pixel and harmonic space and asymptotic uncorrelation. We discuss several statistical applications, including the relation of angular power spectra to the needlet coefficients, testing for non-Gaussianity on polarization data, and reconstruction of the E and B scalar maps.

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