Physically corrected forward operators for induced emission tomography: A simulation study

X-ray emission tomography techniques over non-radioactive materials allow to investigate different and important aspects of the matter that are usually not addressable with the standard X-Ray Transmission Tomography, like: density, chemical composition and crystallographic information. However, the quantitative reconstruction of these investigated properties is hindered by additional problems, including the self-attenuation of the emitted radiation. Work has been done in the past, especially for what concerns X-Ray Fluorescence tomography, but it has always just been focused on solving very specific problems. The novelty of this work resides in addressing the problem of induced emission tomography from a much wider perspective, introducing a unified discrete representation, that can be used to modify existing algorithms to reconstruct the data of the different types of experiments. The direct outcome is a clear and easy mathematical description of the implementation details of such algorithms, despite small differences in geometry and other practical aspects. But also the possibility to express the reconstruction as a minimization problem, allowing the use of variational methods, and a more flexible modeling of the noise involved in the detection process. In addition, we look at the results of a few selected simulated data reconstructions, that describe: the effect of physical corrections like the self-attenuation, and the response to noise of the adapted reconstruction algorithms