INVERSION OF A CLASS OF CIRCULAR AND ELLIPTICAL RADON TRANSFORMS

INVERSION OF A CLASS OF CIRCULAR AND ELLIPTICAL RADON TRANSFORMS
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一类圆椭圆Radon变换的反演

DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
V. Krishnan
V. Krishnan
中科院分区：
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文献类型：
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作者：
G. Ambartsoumian;V. Krishnan

文献摘要

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本文研究了超声成像问题中出现的一类椭圆Radon变换和圆形Radon变换。这些变换对应于2D中的未知图像函数f，其积分Rf沿着 一族椭圆（或圆）。从成像的角度来看，特别感兴趣的是数据采集的圆形几何形状。这里，广义拉东变换R沿沿着椭圆（圆）积分f，其中椭圆的焦点（中心）位于固定圆C上。我们证明了这种变换可以从径向不完全数据中唯一地反演，以恢复环形图像函数。 地区我们的结果适用于f在数据采集圆C的内部和/或外部得到支持的情况。
The paper considers a class of elliptical and circular Radon transforms appearing in problems of ultrasound imaging. These transforms put into correspondence to an unknown image function f in 2D its integrals Rf along a family of ellipses (or circles) . From the imaging point of view, of particular interest is the circular geometry of data acquisition. Here the generalized Radon transform R integrates f along ellipses (circles) with their foci (centers) located on a fixed circle C. We prove that such transforms can be uniquely inverted from radially incomplete data to recover the image function in annular regions. Our results hold for cases when f is supported inside and/or outside of the data acquisition circle C.