Non-linearity in monochromatic transmission tomography

TL;DR

This paper investigates the non-linear nature of monochromatic X-ray tomography caused by extended sources and detectors, demonstrating its effects through experiments and simulations, and proposing an improved reconstruction algorithm.

Contribution

It reveals the non-linearity in monochromatic tomography due to extended sources and detectors and introduces a reconstruction method that accounts for this non-linearity.

Findings

Non-linearity observed in experimental gamma-ray tomography data.

Jacobian matrix of the non-linear forward problem derived.

Enhanced reconstructions achieved using the proposed non-linear method.

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.