Partial inversion of the 2D attenuated $X$-ray transform with data on an arc
Analysis of PDEs
2021-05-12 v4
Abstract
In two dimensions, we consider the problem of inversion of the attenuated -ray transform of a compactly supported function from data restricted to lines leaning on a given arc. We provide a method to reconstruct the function on the convex hull of this arc. The attenuation is assumed known. The method of proof uses the Hilbert transform associated with -analytic functions in the sense of Bukhgeim.
Cite
@article{arxiv.1710.07676,
title = {Partial inversion of the 2D attenuated $X$-ray transform with data on an arc},
author = {Hiroshi Fujiwara and Kamran Sadiq and Alexandru Tamasan},
journal= {arXiv preprint arXiv:1710.07676},
year = {2021}
}
Comments
13 pages, 7 figures