标题： 高速数值阿贝尔变换方法的直接比较 显示英文标题

标题： A direct comparison of high-speed methods for the numerical Abel transform

摘要： 阿贝尔变换是一种数学运算，它将一个圆柱对称的三维 (3D) 物体转化为它的二维投影。 逆阿贝尔变换则从二维投影重建三维物体。 阿贝尔变换在许多科学领域有广泛应用，特别是在化学物理、天文学以及激光等离子体羽流的研究中。 因此，已经开发出许多针对阿贝尔变换的数值方法，这使得为特定应用选择理想方法变得具有挑战性。 在这项工作中，八种变换方法被整合到一个开源的 Python 软件包 (PyAbel) 中，以直接比较每种变换方法的能力、优势和相对计算效率。 大多数测试的方法都提供了类似且高质量的结果。 然而，计算效率在几个数量级上有所不同。 通过优化算法，我们发现某些变换方法足够快，可以在台式个人计算机上以超过每秒 100 帧的速度处理 1 兆像素图像。 此外，我们还演示了千兆像素图像的变换。 显示英文摘要

摘要： The Abel transform is a mathematical operation that transforms a cylindrically symmetric three-dimensional (3D) object into its two-dimensional (2D) projection. The inverse Abel transform reconstructs the 3D object from the 2D projection. Abel transforms have wide application across numerous fields of science, especially chemical physics, astronomy, and the study of laser-plasma plumes. Consequently, many numerical methods for the Abel transform have been developed, which makes it challenging to select the ideal method for a specific application. In this work eight transform methods have been incorporated into a single, open-source Python software package (PyAbel) to provide a direct comparison of the capabilities, advantages, and relative computational efficiency of each transform method. Most of the tested methods provide similar, high-quality results. However, the computational efficiency varies across several orders of magnitude. By optimizing the algorithms, we find that some transform methods are sufficiently fast to transform 1-megapixel images at more than 100 frames per second on a desktop personal computer. In addition, we demonstrate the transform of gigapixel images.