Inversion of seismic-type Radon transforms on the plane
Inversion of seismic-type Radon transforms on the plane
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平面上地震型Radon变换的反演
DOI：
10.1080/10652469.2020.1775202
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发表时间：
2020
影响因子：
1
通讯作者：
Chihara Hiroyuki
中科院分区：
文献类型：
--
作者：
Chihara Hiroyuki;Yasuo Komori-Furuya;Chihara Hiroyuki
我们研究将欧几里得平面上的函数映射到其在平面曲线上的积分族（即平面曲线的函数）的积分变换。我们在本文中考虑的平面曲线是由具有自变量固定轴的函数图给出的，并且相对于轴具有一定的对称性。这些变换包含源自地震学的抛物线Radon变换和双曲Radon变换。我们证明了在函数的某些消失和对称条件下这些变换的反演公式。
We study integral transforms mapping a function on the Euclidean plane to the family of its integration on plane curves, that is, a function of plane curves. The plane curves we consider in the present paper are given by the graphs of functions with a fixed axis of the independent variable and are imposed some symmetry with respect to the axes. These transforms contain the parabolic Radon transform and the hyperbolic Radon transform arising from seismology. We prove the inversion formulas for these transforms under some vanishing and symmetry conditions of functions.