On the Determination of a Function from an Elliptical Radon Transform
Functional Analysis
2013-10-07 v6
Abstract
In recent years, Radon type transforms that integrate functions over various sets of ellipses/ellipsoids have been considered in SAR, ultrasound reflection tomography, and radio tomography. In this paper, we consider the transform that integrates a given function in over a set of solid ellipsoids of rotation with a fixed eccentricity and foci restricted to a hyperplane. Inversion formulas are obtained for appropriate classes of functions that are even with respect to the hyperplane. Stability estimates, range description, and local uniqueness results are also provided.
Cite
@article{arxiv.1302.4396,
title = {On the Determination of a Function from an Elliptical Radon Transform},
author = {Sunghwan Moon},
journal= {arXiv preprint arXiv:1302.4396},
year = {2013}
}