On characterization of the range and inversion formulas for the geodesic X-ray transform
On characterization of the range and inversion formulas for the geodesic X-ray transform
复制标题
测地X射线变换的范围和反演公式的表征
DOI：
10.1155/s1073792804142116
复制
发表时间：
2004
影响因子：
1
通讯作者：
G. Uhlmann
中科院分区：
文献类型：
--
作者：
L. Pestov;G. Uhlmann
我们描述了简单的，二维紧致黎曼流形的边界之间的散射关系，希尔伯特变换在频率空间，测地线射线变换。我们使用这种关系给出的范围内的测地线X射线变换作用于标量函数和矢量场的散射关系，其中只涉及在边界处的测量的表征。我们还给出了测地X射线变换作用于标量函数和向量场的反演公式。
We describe a relation between the scattering relation, the Hilbert transform in frequency space, and the geodesic ray transform for simple, two-dimensional compact Riemannian manifolds with boundary. We use this relation to give a characterization of the range of the geodesic X-ray transform acting on scalar functions and vector fields in terms of the scattering relation which involves only measurements at the boundary. We also give inversion formulas for the geodesic X-ray transform acting on scalar functions and vector fields.