AI 中文总结
针对南希·格雷斯·罗曼太空望远镜原始图像欠采样问题，介绍新算法{\sc Effortless}，其能使点扩散函数更均匀规则，控制系统误差效果更好。本文详述其数学形式、软件实现等，该接口通用，可支持更多用例。
AI 中文摘要
弱引力透镜是一种很有前景但技术要求很高的宇宙学探测方法。对于即将到来的南希·格雷斯·罗曼太空望远镜这样的太空任务来说，一个主要挑战是原始图像欠采样，需要进行重建以实现精确测量。{\sc Effortless}（使用更少内存的高效最优图像重建；以前称为快速{\sc Imcom}）就是为此设计的新算法。之前的论文已展示出初步成果，表明{\sc Effortless}能比其前身{\sc Imcom}更有效地使重建图像上的点扩散函数（PSF）均匀且规则，在控制系统误差方面也有超越{\sc Imcom}的潜力。本文详细介绍了其数学形式、软件实现及实际问题。首先，虽然奈奎斯特 - 香农采样定理仍然成立，但定理条件与测量数据处理问题略有不同，通过简单的测量后校准可大幅降低有限采样效应。数值伪像、输入像素窗口有限性和一些输入像素不可用所导致的缺陷已得到理解和控制。{\sc Effortless}应用程序编程接口具有通用性，可支持弱引力透镜宇宙学及罗曼太空望远镜之外的用例。
英文摘要
Weak gravitational lensing is a promising but technically demanding cosmological probe. For space missions like the forthcoming Nancy Grace Roman Space Telescope, a major challenge is that native images are undersampled and need to be reconstructed to enable accurate measurements. {\sc Effortless} (EFFicient Optimal image ReconsTruction using LESS memory; previously known as Fast {\sc Imcom}) is a new algorithm designed for that purpose. My companion paper has exhibited promising first results to demonstrate that {\sc Effortless} can make point spread functions (PSFs) uniform and regular across reconstructed images more efficiently than its predecessor {\sc Imcom} and has the potential to outperform {\sc Imcom} in terms of control over systematic errors. In this paper, I present the mathematical formalism, software implementation, and practical issues in detail. Foremost, while the Nyquist--Shannon sampling theorem remains true, the conditions of the theorem are subtly (and importantly) different from the problem in survey data processing, and finite sampling effects can be substantially reduced via a simple post-measurement calibration. Imperfections caused by numerical artifacts, finiteness of input pixel windows, and unavailability of some input pixels are understood and under control. The {\sc Effortless} application programming interface is general and can support use cases beyond weak lensing cosmology and beyond the Roman Space Telescope.
Comments28 pages, 15 figures, submitted to ApJS
