We were pleased to have Prof. Fatma Terzioglu visiting from North Carolina State University, where she serves as an assistant professor in the Department of Mathematics at NC State. Prior to joining NC State, she was a W. H. Kruskal Instructor at the University of Chicago, where she worked with Guillaume Bal. She received her Ph.D. in Mathematics from Texas A&M University in 2018, advised by Peter Kuchment. Her research focuses on developing analytic and computational methods for inverse problems arising in imaging sciences (e.g., medical, industrial, and homeland security imaging). You can read more about her work on her personal page.
Prof. Terzioglu shared about her research on modeling, invertibility, and parameter design in multi-energy (spectral) computed tomography as part of a joint AWM Seminar and Mathematical Sciences Department Colloquium. After the presentation, she joined attendees for a tea time in the Stratton Hall Faculty Lounge.
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.