Fast convolution on the sphere
Fast convolution on the sphere
复制标题
球体上的快速卷积
DOI：
10.1103/physrevd.63.123002
复制
发表时间：
2000
影响因子：
5
通讯作者：
K. Gorski
中科院分区：
文献类型：
--
作者：
B. Wandelt;K. Gorski
华沙大学天文台，华沙，波兰（2008年2月1日）我们提出了快速，准确和高效的算法卷积的两个任意函数onthe球，加快计算的一个因素O <$N相比，目前的方法，其中N是像素的数量。除了带宽限制之外，没有做任何简化的假设。这减少了典型的计算时间卷积全天空与不对称光束图案的百万像素宇宙微波背景（CMB）的使命从几个月到几分钟。我们的方法是可行的现实模拟和仔细分析这些任务的数据，考虑到不对称的“点扩散函数”和远旁瓣的物理光束的三个方面。在CMB研究的激励下，我们的方法是通用的，因此适用于具有任意非对称核的球体上的任何标量场的卷积或滤波。我们在附录中表明，同样的想法可以应用于映射和波束重建的逆问题，通过类似地加速正规方程迭代求解所需的转置卷积。介绍
Warsaw University Observatory, Warsaw, Poland(February 1, 2008)We propose fast, exact and efficient algorithms for the convolution of two arbitrary functions onthe sphere which speed up computations by a factor O √Ncompared to present methods whereN is the number of pixels. No simplifying assumptions are made other than bandlimitation. Thisreduces typical computation times for convolving the full sky with the asymmetric beam pattern ofa megapixel Cosmic Microwave Background (CMB) mission from months to minutes. Our methodsenable realistic simulation and careful analysis of data from such missions, taking into account theeffects of asymmetric “point spread functions” and far side lobes of the physical beam. Whilemotivated by CMB studies, our methods are general and hence applicable to the convolution orfiltering of any scalar field on the sphere with an arbitrary, asymmetric kernel. We show in anappendix that the same ideas can be applied to the inverse problems of map-making and beamreconstruction by similarly accelerating the transpose convolution which is needed for the iterativesolution of the normal equations.I. INTRODUCTION