Inversion of the circular Radon transform on an annulus
Inversion of the circular Radon transform on an annulus
复制标题
环面上圆形 Radon 变换的反演
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
M. Lewis
中科院分区：
文献类型：
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作者：
G. Ambartsoumian;R. Gouia;M. Lewis
函数的圆形Radon变换（CRT）表示及其相关问题在数学、物理和成像科学的许多领域都有出现。在过去的十年里，由于CRT和一些新兴医学成像模式的数学模型之间的联系，人们对这些问题的兴趣激增。本文给出了用部分数据的阴极射线管表示函数的存在唯一性的一些新结果。本文提出了一种新的反演公式，适用于内部和外部问题的圆形采集几何，当Radon变换仅对所有可能半径的一部分已知时。结果不仅是有趣的原始数学发现，但也可以用于应用，例如，在医学成像。
The representation of a function by its circular Radon transform (CRT) and various related problems arise in many areas of mathematics, physics and imaging science. There has been a substantial spike of interest toward these problems in the last decade mainly due to the connection between the CRT and mathematical models of several emerging medical imaging modalities. This paper contains some new results about the existence and uniqueness of the representation of a function by its CRT with partial data. A new inversion formula is presented in the case of the circular acquisition geometry for both interior and exterior problems when the Radon transform is known for only a part of all possible radii. The results are not only interesting as original mathematical discoveries, but can also be useful for applications, e.g., in medical imaging.