Non-linearity in monochromatic transmission tomography
Abstract
While it is well known that X-ray tomography using a polychromatic source is non-linear, as the linear attenuation coefficient depends on the wavelength of the X-rays, tomography using near monochromatic sources are usually assumed to be a linear inverse problem. When sources and detectors are not treated as points the measurements are the integrals of the exponentials of line integrals and hence non-linear. In this paper we show that this non-linearity can be observed in realistic situations using both experimental measurements in a gamma-ray tomography system and simulations. We exhibit the Jacobian matrix of the non-linear forward problem. We also demonstrate a reconstruction algorithm, which we apply to experimental data and we show that improved reconstructions can be obtained over the linear approximation.
Cite
@article{arxiv.1705.05160,
title = {Non-linearity in monochromatic transmission tomography},
author = {William R. B. Lionheart and Bjørn Tore Hjertaker and Rachid Maad and Ilker Meric and Sophia B. Coban and Geir Anton Johansen},
journal= {arXiv preprint arXiv:1705.05160},
year = {2017}
}