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arXiv 1109.0286astro-ph.CO
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使用约束高斯实现填充CMB地图缺失数据

Filling in CMB map missing data using constrained Gaussian realizations

Martin Bucher, Thibaut Louis

摘要:

为了分析宇宙微波背景的天空图,有必要遮蔽银河赤道周围的区域,那里的寄生前景发射是最强的,以及最明亮的紧凑源。由于许多数据的分析,特别是那些寻找原始起源的非高斯性的分析,是最直接地在全天空地图上进行的,因此开发有效的算法以合理的方式填充缺失的信息是非常有趣的。我们探索实用的算法填充约束高斯实现的基础上。虽然实现这样的实现原则上是简单的,但对于普朗克分析所需的精细像素化地图,直接的蛮力方法在数值上是不容易处理的。我们提出了一些具体的解决方案,这个问题,无论是在一个空间平坦的天空周期性的边界条件和像素化的领域。一种方法是用适当预处理的共轭梯度法求解线性方程组。虽然这种方法在具有周期性边界条件的矩形域上成功实现,并且即使对于非常宽的掩蔽区域也有效,但我们发现该方法在像素化球体上失败,原因我们在这里解释。我们提出了一种方法,适用于全天空像素化的地图上的球体涉及一个基于内核的多分辨率拉普拉斯求解器,其次是一系列的共轭梯度校正附近的边界的面具。

英文摘要:

For analyzing maps of the cosmic microwave background sky, it is necessary to mask out the region around the galactic equator where the parasitic foreground emission is strongest as well as the brightest compact sources. Since many of the analyses of the data, particularly those searching for non-Gaussianity of a primordial origin, are most straightforwardly carried out on full-sky maps, it is of great interest to develop efficient algorithms for filling in the missing information in a plausible way. We explore practical algorithms for filling in based on constrained Gaussian realizations. Although carrying out such realizations is in principle straightforward, for finely pixelized maps as will be required for the Planck analysis a direct brute force method is not numerically tractable. We present some concrete solutions to this problem, both on a spatially flat sky with periodic boundary conditions and on the pixelized sphere. One approach is to solve the linear system with an appropriately preconditioned conjugate gradient method. While this approach was successfully implemented on a rectangular domain with periodic boundary conditions and worked even for very wide masked regions, we found that the method failed on the pixelized sphere for reasons that we explain here. We present an approach that works for full-sky pixelized maps on the sphere involving a kernel-based multi-resolution Laplace solver followed by a series of conjugate gradient corrections near the boundary of the mask.

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