标题： 小波在宇宙微波背景图分析中的应用 显示英文标题

标题： Applications of Wavelets to the Analysis of Cosmic Microwave Background Maps

摘要： 我们考虑将小波作为工具，在分析宇宙微波背景（CMB）图的背景下执行各种任务。 使用球面哈尔小波，我们定义了一个与位置和角尺度相关的功率度量，可用于评估空间结构的存在。 我们使用平面多贝希小波来识别和去除天空图的小区域中的点源。 我们的技术可以成功识别几乎所有高于3倍标准差的点源以及超过80%的高于1倍标准差的点源。 我们讨论了正确检测和错误检测之间的权衡。 我们通过约10倍的压缩在5秒内对一个100,000像素的CMB图进行去噪和压缩，实现了约35%的噪声降低。 与维纳滤波相比，压缩过程是模型无关且非常快速的。 我们讨论了小波在功率谱和宇宙学参数估计中的有用性。 我们得出结论，目前小波函数最适合用于识别局部源。 显示英文摘要

摘要： We consider wavelets as a tool to perform a variety of tasks in the context of analyzing cosmic microwave background (CMB) maps. Using Spherical Haar Wavelets we define a position and angular-scale-dependent measure of power that can be used to assess the existence of spatial structure. We apply planar Daubechies wavelets for the identification and removal of points sources from small sections of sky maps. Our technique can successfully identify virtually all point sources which are above 3 sigma and more than 80% of those above 1 sigma. We discuss the trade-offs between the levels of correct and false detections. We denoise and compress a 100,000 pixel CMB map by a factor of about 10 in 5 seconds achieving a noise reduction of about 35%. In contrast to Wiener filtering the compression process is model independent and very fast. We discuss the usefulness of wavelets for power spectrum and cosmological parameter estimation. We conclude that at present wavelet functions are most suitable for identifying localized sources.