Inversion of Higher Dimensional Radon Transforms of Seismic-Type
Inversion of Higher Dimensional Radon Transforms of Seismic-Type
复制标题
地震型高维氡变换反演
DOI：
10.1007/s10013-020-00446-8
复制
发表时间：
2020
影响因子：
0.8
通讯作者：
Chihara Hiroyuki
中科院分区：
文献类型：
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作者：
Chihara Hiroyuki
我们研究积分变换，将欧几里得空间上的函数映射到其在某些超曲面上的积分族，即超曲面的函数。超曲面由具有自变量固定轴的函数图给出，并且相对于轴具有一定的对称性。这些变换是由地震学产生的抛物线 Radon 变换和双曲 Radon 变换的推广的高维版本。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 space to the family of its integration on some hypersurfaces, that is, a function of hypersurfaces. The hypersurfaces are given by the graphs of functions with fixed axes of the independent variables, and are imposed some symmetry with respect to the axes. These transforms are higher dimensional version of generalization of 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.