科学驱动的3D数据压缩
Science-driven 3D data compression
摘要：
测光红移巡天通过星系的位置和形状来绘制宇宙中物质的分布图，但对星系的径向坐标的测量分辨率很低。虽然层析分析可以用来恢复数据中存在的一些大规模径向模式，但这种方法存在许多实际缺点，并且决定特定分箱方案的标准通常对最终的科学目标视而不见。我们提出了一种方法，旨在分离和压缩成少量的不相关的径向模式的数据，规避了一些标准的层析分析的问题。该方法是基于Karhunen-Loève变换（KL），并连接到其他的三维数据压缩基础的文献中提倡，如傅立叶-贝塞尔分解。我们将这种方法应用到弱透镜和星系团。在星系聚类的情况下，我们表明，由此产生的最佳基础是密切相关的傅里叶-贝塞尔基础，并为某些可观的，如放大率偏置或原始非高斯的影响，大部分的信号可以被压缩成少量的模式。在弱透镜的情况下，我们表明，该方法是能够压缩到一个单一的模式的信号噪声的绝大多数，最佳的宇宙学约束可以得到考虑只有三个不相关的KL本征模，大大简化了分析相对于传统的层析方法。
英文摘要：
Photometric redshift surveys map the distribution of matter in the Universe through the positions and shapes of galaxies with poorly resolved measurements of their radial coordinates. While a tomographic analysis can be used to recover some of the large-scale radial modes present in the data, this approach suffers from a number of practical shortcomings, and the criteria to decide on a particular binning scheme are commonly blind to the ultimate science goals. We present a method designed to separate and compress the data into a small number of uncorrelated radial modes, circumventing some of the problems of standard tomographic analyses. The method is based on the Karhunen-Loève transform (KL), and is connected to other 3D data compression bases advocated in the literature, such as the Fourier-Bessel decomposition. We apply this method to both weak lensing and galaxy clustering. In the case of galaxy clustering, we show that the resulting optimal basis is closely associated with the Fourier-Bessel basis, and that for certain observables, such as the effects of magnification bias or primordial non-Gaussianity, the bulk of the signal can be compressed into a small number of modes. In the case of weak lensing we show that the method is able to compress the vast majority of the signal-to-noise into a single mode, and that optimal cosmological constraints can be obtained considering only three uncorrelated KL eigenmodes, considerably simplifying the analysis with respect to a traditional tomographic approach.
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