论文标题
快速星系卷积的混合傅里叶 - 现实的高斯混合物方法
A hybrid Fourier--Real Gaussian Mixture method for fast galaxy--PSF convolution
论文作者
论文摘要
我提出了一种通过点传播函数（PSF）模型（表示为像素网格）快速卷积的方法。该方法依赖于三个观察：首先，最简单的共同兴趣（devaucouleurs，oppertential，sersic）的径向径向星系概况可以近似为高斯的混合物。其次，高斯的傅立叶变换是高斯人，因此可以直接评估Gausssian的混合物的傅立叶变换，以作为高斯在傅立叶空间中的混合物进行评估。第三，如果混合组件会导致傅立叶空间混叠，则可以在真实空间中评估该组件。对于要在傅立叶空间中评估的混合组件，我们将FFT用于PSF模型，直接评估银河系的傅立叶变换，而逆FFF将结果返回到像素空间。对于在真实空间中进行评估的混合物组件 - 仅在混合组件大得多的PSF大得多时才发生 - 我们使用PSF的简单高斯近似值，分析进行卷积并在实际像素空间中进行评估。该方法是快速而精确的（只要对像素化的PSF模型进行了充分的采样，高斯的混合物的近似值是精确的。这种傅立叶方法可以看作是将完美的低通滤波器应用于PSF卷积之前（通常是强烈采样）的星系剖面，以PSF PSF像素模型网格的确切频率。通过这种方式，它避免了传统的超分辨率方法的计算费用。该方法允许在Galaxy正向模型拟合方法（例如拖拉机）中有效使用像素化的PSF模型（即，以像素值表示为像素值的网格）。
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.
