Orthogonal function series formulae for inversion of the conical Radon transform with a fixed central axis

摘要

In this study, we derive two new inversion formulae for the n??+??1-dimensional conical Radon transform that integrates a given n??+??1-dimensional function on the upper half space over all conical surfaces with vertices on a hyperplane and a central axis orthogonal to this hyperplane: both formulae are based on the orthonormal bases of certain Hilbert spaces. One formula is derived from a singular value decomposition, a valuable tool in the study of ill-posed problems, of the conical Radon transform.