快速星系的混合傅里叶-实高斯混合方法-- PSF卷积
A hybrid Fourier--Real Gaussian Mixture method for fast galaxy--PSF convolution
摘要：
我提出了一个快速卷积的模型星系轮廓的点扩散函数（PSF）模型表示为一个像素网格的方法。该方法依赖于三个观测：第一，最简单的径向星系配置文件的共同利益（deVaucouleurs，指数，Sersic）可以近似为高斯的混合物。其次，高斯的傅立叶变换也是高斯的，因此星系的混合高斯近似的傅立叶变换可以直接被评估为傅立叶空间中的高斯混合。第三，如果混合成分会导致傅立叶空间混叠，则可以在实空间中评估该成分。对于要在傅立叶空间中评估的混合成分，我们使用FFT用于PSF模型，直接评估星系的傅立叶变换，并使用逆FFT将结果返回到像素空间。对于要在实空间中计算的混合分量-这只发生在混合分量比PSF大得多的时候-我们使用PSF的简单高斯近似，分析地执行卷积，并在实像素空间中计算。该方法是快速和准确的（在某种程度上，混合高斯近似的星系轮廓是准确的），只要像素化的PSF模型是很好的采样。这种傅立叶方法可以被看作是一种在PSF卷积之前对（通常是强烈欠采样的）星系轮廓应用完美低通滤波器的方法，精确地在PSF像素模型网格的奈奎斯特频率处。通过这种方式，它避免了传统超分辨率方法的计算开销。这种方法允许在星系前向模型拟合方法（如Tractor）中有效使用像素化PSF模型（即，表示为像素值网格的PSF）。
英文摘要：
I present a method for the fast convolution of a model galaxy profile by a point-spread function (PSF) model represented as a pixel grid. The method relies upon three observations: First, most simple radial galaxy profiles of common interest (deVaucouleurs, exponential, Sersic) can be approximated as mixtures of Gaussians. Second, the Fourier transform of a Gaussian is a Gaussian, thus the Fourier transform of a mixture-of-Gausssian approximation of a galaxy can be directly evaluated as a mixture of Gaussians in Fourier space. Third, if a mixture component would result in Fourier-space aliasing, that component can be evaluated in real space. For mixture components to be evaluated in Fourier space, we use the FFT for the PSF model, direct evaluation of the Fourier transform for the galaxy, and the inverse-FFT to return the result to pixel space. For mixture components to be evaluated in real space---which only happens when the mixture components is much larger than the PSF---we use a simple Gaussian approximation of the PSF, perform the convolution analytically, and evaluate in real pixel space. The method is fast and exact (to the extent that the mixture-of-Gaussians approximation of the galaxy profile is exact) as long as the pixelized PSF model is well sampled. This Fourier method can be seen as a way of applying a perfect low-pass filter to the (typically strongly undersampled) galaxy profile before convolution by the PSF, at exactly the Nyquist frequency of the PSF pixel model grid. In this way, it avoids the computational expense of a traditional super-resolution approach. This method allows the efficient use of pixelized PSF models (ie, a PSF represented as a grid of pixel values) in galaxy forward model-fitting approaches such as the Tractor.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
