Multi-energy computed tomography (ME-CT) is an x-ray transmission imaging technique that uses the energy dependence of x-ray photon attenuation to determine the elemental composition of an object of interest. Mathematically, forward ME-CT measurements are modeled by a nonlinear integral transform. In this paper, local conditions for global invertibility of the ME-CT transform are studied, and explicit stability estimates quantifying the error propagation from measurements to reconstructions are provided. Motivated from the inverse problem of image reconstruction in ME-CT, an iterative inversion algorithm for the so-called P-functions is proposed. Numerical simulations for ME-CT, in two and three materials settings with an equal number of energy measurements, confirm the theoretical predictions.
@article{arxiv.2110.01405,
title = {An inversion algorithm for P-functions with applications to Multi-energy CT},
author = {Guillaume Bal and Ruoming Gong and Fatma Terzioglu},
journal= {arXiv preprint arXiv:2110.01405},
year = {2022}
}