Department of Mathematical Sciences
Colloquium
Friday, November 21st, 2025
11:00AM-11:50AM
Stratton Hall 202
Speaker: Fatma Terzioglu, North Carolina State University
Title: From Conventional CT to Multi-Energy CT: Modeling, Invertibility, and Parameter Design
Abstract: Multi-energy (spectral) computed tomography is an advanced x-ray imaging modality that not only reveals the morphology of the examined object, but also its underlying elemental composition. It takes advantage of the fact that different materials attenuate x-rays in an energy-dependent manner and uses this information to recover material identities. Mathematically, however, the measured data are related to the unknown object through a nonlinear integral transform which, unlike in conventional CT, does not admit a closed-form inversion. In this talk, I will first introduce the mathematical model for x-ray CT and its extension to multi-energy CT, and then I will present a framework for determining when this nonlinear transform is globally injective and for quantifying the stability of its inversion. I will also discuss how these results inform the selection of scan parameters so that the reconstruction problem is as well-posed as possible. The talk will conclude with numerical experiments illustrating the theoretical findings and some directions for further research.