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arXiv 1204.4293astro-ph.CO
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弱透镜孔径质量统计的快速计算

Fast Calculation of the Weak Lensing Aperture Mass Statistic

Adrienne Leonard, Sandrine Pires, Jean-Luc Starck

摘要:

孔径质量统计是弱透镜研究中常用的工具。通过将透镜化映射与特定尺度的滤波器函数进行卷积,透镜化信号可以相对于噪声被提升,该特定尺度被选择为大于噪声占主导地位的尺度。这允许以增加的保真度检测结构。此外,孔径质量的高阶统计(如其偏度或峰度),或在所得孔径质量图中看到的峰值的计数,提供了一种方便有效的方法来约束宇宙学参数。在本文中,我们更充分地探讨了形式主义背后的光圈质量统计。我们证明,孔径质量统计是正式相同的小波变换在一个特定的尺度。此外,我们表明,最常用的孔径质量研究中的过滤功能是不理想的,是非本地的真实和傅立叶空间。相比之下,小波形式主义提供了一些小波函数,这些小波函数在实空间和傅立叶空间都是局部的,但类似于通常采用的“最佳”孔径质量滤波器。此外,对于许多小波函数,例如星小波,存在非常快速的算法来计算小波变换。在图像处理时间方面,这比通常的孔径质量算法具有显著优势,在1024 x 1024像素的图像上,孔径半径在2至64像素范围内的加速因子约为5 - 1200。

英文摘要:

The aperture mass statistic is a common tool used in weak lensing studies. By convolving lensing maps with a filter function of a specific scale, chosen to be larger than the scale on which the noise is dominant, the lensing signal may be boosted with respect to the noise. This allows for detection of structures at increased fidelity. Furthermore, higher-order statistics of the aperture mass (such as its skewness or kurtosis), or counting of the peaks seen in the resulting aperture mass maps, provide a convenient and effective method to constrain the cosmological parameters. In this paper, we more fully explore the formalism underlying the aperture mass statistic. We demonstrate that the aperture mass statistic is formally identical to a wavelet transform at a specific scale. Further, we show that the filter functions most frequently used in aperture mass studies are not ideal, being non-local in both real and Fourier space. In contrast, the wavelet formalism offers a number of wavelet functions that are localized both in real and Fourier space, yet similar to the 'optimal' aperture mass filters commonly adopted. Additionally, for a number of wavelet functions, such as the starlet wavelet, very fast algorithms exist to compute the wavelet transform. This offers significant advantages over the usual aperture mass algorithm when it comes to image processing time, demonstrating speed-up factors of ~ 5 - 1200 for aperture radii in the range 2 to 64 pixels on an image of 1024 x 1024 pixels.

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