SIAM Journal on Imaging Sciences, Volume 14, Issue 3, Page 1004-1038, January 2021.
We propose a novel direct sampling method (DSM) for the effective and stable inversion of the Radon transform. The DSM is based on a generalization of the important almost orthogonality property in classical DSMs to fractional order Sobolev duality products and to a new family of probing functions. The fractional order duality product proves to be able to greatly enhance the robustness of the reconstructions in some practically important but severely ill-posed inverse problems associated with the Radon transform. We present a detailed analysis to better understand the performance of the new probing and index functions, which are crucial to stable and effective numerical reconstructions. The DSM can be computed in a very fast and highly parallel manner. Numerical experiments are carried out to compare the DSM with a popular existing method and to illustrate the efficiency, stability, and accuracy of the DSM.

中文翻译：

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Radon变换反演的一种直接采样方法

SIAM 成像科学杂志，第 14 卷，第 3 期，第 1004-1038 页，2021 年 1 月。
我们提出了一种新颖的直接采样方法 (DSM)，用于有效且稳定地反演 Radon 变换。DSM 基于将经典 DSM 中重要的几乎正交性属性推广到分数阶 Sobolev 对偶乘积和新的探测函数系列。分数阶对偶乘积证明能够在与 Radon 变换相关的一些实际重要但严重不适定的逆问题中大大增强重建的鲁棒性。我们进行了详细分析，以更好地了解新探测和索引函数的性能，这对于稳定有效的数值重建至关重要。DSM 可以以非常快速和高度并行的方式计算。