发表机构
Dragonfly Focused Research Organization; Centre de recherche en astrophysique du Québec (CRAQ); Yale University; University of Toronto; NRC Herzberg Astronomy & Astrophysics Research Centre; Leiden University（龙焦点研究组织; 魁北克天体物理研究中心; 耶鲁大学; 多伦多大学; NRC赫茨伯格天文与天体物理研究中心; 莱顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出双核优化算法，通过同时优化两个卷积核实现PSF匹配并最小化核尺寸，利用SGLD解决高度退化问题，适用于PSF方向或形状不同的图像。
AI 中文摘要
标准的点扩散函数（PSF）匹配算法将一幅图像视为参考图像，并旨在找到一个卷积核，使得当将该核应用于参考图像时，参考图像和非参考图像的PSF得以匹配。如果一幅图像是另一幅图像的退化版本，这种方法效果良好。然而，情况并非总是如此：如果两幅图像的PSF具有不同的方向或形状，对其中一幅图像进行简单卷积并不能获得令人满意的匹配。虽然可以通过将第一个PSF与第二个卷积以及反之亦然来简单解决，但这会导致不必要的庞大PSF。在本文中，我们提出了一种新算法——双核优化（DKO），该算法同时求解两个卷积核，每个图像一个，使得PSF匹配且核的尺寸最小化。这导致最终PSF集合的退化程度最小。由于该问题高度退化，我们使用随机梯度Langevin动力学（SGLD），该算法严格探索参数空间并收敛于全局最优解。我们讨论了该问题的算法挑战以及对标准SGLD所做的修改以约束该问题。最后，我们讨论了该方法在实际图像中的应用，包括PSF在视场上变化的情况。
英文摘要
Standard point spread function (PSF) matching algorithms consider one image as the reference and aim to find a convolution kernel such that, when applied to the reference image, the PSFs of the reference and non-reference images are matched. This method works well if one image is a degraded version of the other. However, this is not always the case: if the PSFs of the two images have different orientations or shapes, a simple convolution of one of the images does not lead to a satisfactory match. While this can be trivially solved by convolving the first PSF with the second and vice-versa, this results in unnecessarily large PSFs. In this paper, we present a new algorithm, Dual Kernel Optimization (DKO), that simultaneously solves for two convolution kernels, one for each image, such that the PSFs match and the sizes of the kernels are minimized. This results in a minimally-degraded final set of PSFs. Since this problem is highly degenerate, we use Stochastic Gradient Langevin Dynamics (SGLD) which rigorously explores the parameter space and converges on the globally-optimal solution.We discuss the algorithmic challenges for this problem and the modifications to standard SGLD used to constrain it. Finally, we include a discussion on the application of this methodology to real-world images, including cases where the PSF varies over the field of view.
CommentsAccepted in RASTI; The associated Python module, including demos and documentation, can be found at https://github.com/DragonflyTelescope/dfpsf
