Inversion of Weighted Divergent Beam and Cone Transforms
Numerical Analysis
2016-12-23 v2 Functional Analysis
Abstract
In this paper, we investigate the relations between the Radon and weighted divergent beam and cone transforms. Novel inversion formulas are derived for the latter two. The weighted cone transform arises, for instance, in image reconstruction from the data obtained by Compton cameras, which have promising applications in various fields, including biomedical and homeland security imaging and gamma ray astronomy. The inversion formulas are applicable for a wide variety of detector geometries in any dimension. The results of numerical implementation of some of the formulas in dimensions two and three are also provided.
Keywords
Cite
@article{arxiv.1612.06772,
title = {Inversion of Weighted Divergent Beam and Cone Transforms},
author = {Peter Kuchment and Fatma Terzioglu},
journal= {arXiv preprint arXiv:1612.06772},
year = {2016}
}