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

Area of Science:

• * Mathematical physics
• * Applied optics
• * Plasma physics

Background:

• * The Abel transform and its inverse are crucial for reconstructing 3D objects from 2D projections.
• * Applications span chemical physics, astronomy, and laser-plasma plume studies.
• * Numerous numerical methods exist, complicating selection for specific applications.

Purpose of the Study:

• * To create an open-source Python package (PyAbel) for comparing Abel transform methods.
• * To evaluate the capabilities, advantages, and computational efficiency of eight published methods.
• * To guide users in selecting the optimal Abel transform algorithm for their research.

Main Methods:

• * Implementation of eight distinct Abel transform algorithms within the PyAbel software.
• * Comparative analysis of algorithm performance, focusing on accuracy and computational speed.
• * Optimization of algorithms to assess maximum achievable processing rates.

Main Results:

• * Most tested Abel transform methods produce comparable, high-fidelity reconstructions.
• * Significant variations in computational efficiency were observed across the methods.
• * Optimized algorithms achieve speeds exceeding 100 frames per second for 1-megapixel images.

Conclusions:

• * PyAbel provides a valuable tool for method selection in Abel transform applications.
• * Computational efficiency is a key differentiator among Abel transform algorithms.
• * The developed methods support real-time processing of large-scale imaging data.