基于切比雪夫有理函数的图像分析新工具：CHEF函数
A new tool for image analysis based on Chebyshev rational functions: CHEF functions
摘要：
我们介绍了一种新的方法来模拟星系的光分布，一个正交极基的切比雪夫有理函数和傅立叶多项式的组合，我们称之为CHEF函数，或CHEFs。我们已经开发了一个正交化过程，将此基础应用于像素化图像，并将该方法作为Python管道实现。新的基础显示出非凡的灵活性，能够准确地适应各种星系的形状，包括不规则星系，螺旋星系，椭圆星系，高度紧凑和高度细长的星系。它这样做，同时使用更少的组件，类似的方法，如shapeling，并没有产生文物，由于合理的切比雪夫多项式的效率，以适应快速衰减的功能，如星系轮廓。该方法是线性的，非常稳定，因此能够以快速和自动化的方式处理大量的星系。由于高质量的适合在星系的中心部分，和效率的CHEF基础上建模星系轮廓非常大的距离，该方法提供了高度准确的估计总星系通量和椭圆。未来的论文将更详细地探讨该方法的应用，以执行多波段测光，形态分类和弱剪切测量。
英文摘要：
We introduce a new approach to the modelling of the light distribution of galaxies, an orthonormal polar base formed by a combination of Chebyshev rational functions and Fourier polynomials that we call CHEF functions, or CHEFs. We have developed an orthonormalization process to apply this basis to pixelized images, and implemented the method as a Python pipeline. The new basis displays remarkable flexibility, being able to accurately fit all kinds of galaxy shapes, including irregulars, spirals, ellipticals, highly compact and highly elongated galaxies. It does this while using fewer components that similar methods, as shapelets, and without producing artifacts, due to the efficiency of the rational Chebyshev polynomials to fit quickly decaying functions like galaxy profiles. The method is lineal and very stable, and therefore capable of processing large numbers of galaxies in a fast and automated way. Due to the high quality of the fits in the central parts of the galaxies, and the efficiency of the CHEF basis modeling galaxy profiles up to very large distances, the method provides highly accurate estimates of total galaxy fluxes and ellipticities. Future papers will explore in more detail the application of the method to perform multiband photometry, morphological classification and weak shear measurements.
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