An approach to the spherical mean Radon transform with detectors on a line
Numerical Analysis
2017-05-31 v1
Abstract
The article suggests a new approach what is called a consistency method for the inversion of the spherical Radon transform in 2D with detectors on a line. It is known that there is not an exact inversion formula in 2D. By means of the method was proved that the reconstruction has a local description and found a new iteration formula which give an practical algorithm to recover an unknown function supported completely on one side of a line from its spherical means over circles centered on the line . Such an inversion is required in problems of thermo- and photo-acoustic tomography.
Keywords
Cite
@article{arxiv.1705.10690,
title = {An approach to the spherical mean Radon transform with detectors on a line},
author = {Rafik Aramyan},
journal= {arXiv preprint arXiv:1705.10690},
year = {2017}
}