Ray Transforms on a Conformal Class of Curves
Complex Variables
2010-11-12 v3 Analysis of PDEs
Abstract
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields defining the initial transport and recasting the problem in terms of complex-analytic function theory. Explicit inversion formulae are then given in a unified form. The method is then used to give inversion formulae for the attenuated ray transform.
Keywords
Cite
@article{arxiv.1011.0453,
title = {Ray Transforms on a Conformal Class of Curves},
author = {Nicholas Hoell and Guillaume Bal},
journal= {arXiv preprint arXiv:1011.0453},
year = {2010}
}
Comments
This paper has been withdrawn by the authors. Withdrawn to add references