论文标题
一种直接采样方法，用于反转ra倒转换
A Direct Sampling Method for the Inversion of the Radon Transform
论文作者
论文摘要
我们提出了一种新型的直接采样方法（DSM），以进行ra换的有效和稳定反转。 DSM基于对经典DSM中重要的几乎正交性属性的概括，以分数sobolev二元产品和新的探测功能家族。事实证明，分数阶二元产品能够在某些与ra transform换相关的实际重要但严重的反问题中大大增强重建的鲁棒性。我们提供了详细的分析，以更好地了解新的探测功能的性能，这对于稳定且有效的数值重建至关重要。 DSM可以以非常快速且高度平行的方式计算。进行数值实验以将DSM与流行的现有方法进行比较，并说明DSM的效率，稳定性和准确性。
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.
