Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra
Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra
复制标题
从中心位于某些多边形和多面体表面上的球（圆形）函数重建函数
DOI：
10.1088/0266-5611/27/2/025012
复制
发表时间：
2010
期刊：
影响因子：
2.1
通讯作者：
L. Kunyansky
中科院分区：
文献类型：
--
作者：
L. Kunyansky
我们提出了明确的过滤/反投影型公式的球形（圆形）的平均变换的反演与中心位于一些多面体（或多边形，在2D）的边界上。公式推导出使用双层势的波动方程，具有一定的对称性的域。该公式适用于二维的矩形和某些三角形，以及三维的长方体、某些直角棱柱和某些棱锥。所有目前的反演公式产生精确的重建内的域所包围的采集表面，即使在存在外部源。
We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the double-layer potentials for the wave equation, for domains with certain symmetries. The formulae are valid for a rectangle and certain triangles in 2D, and for a cuboid, certain right prisms and a certain pyramid in 3D. All the present inversion formulae yield exact reconstruction within the domain surrounded by the acquisition surface even in the presence of exterior sources.
影响因子：
3.8
作者：
Kruger, RA;Reinecke, DR;Kruger, GA
通讯作者：
Kruger, GA