The HADES seminar on Tuesday, September 28th, will be given by Joey Zou at 5 pm in 740 Evans.
Speaker: Joey Zou (University of California, Santa Cruz)
Abstract: In X-ray CT scans with metallic objects, streak artifacts in the computed image may arise due to beam hardening effects, where the attenuation coefficient of metallic objects vary strongly with energy. A mathematical description of these artifacts using the notion of wavefront sets was given by Choi, Park, and Seo in 2014, followed by the work of Palacios, Uhlmann, and Wang, who gave quantitative descriptions of the artifacts that recovered qualitative observations from CT scans when the metallic objects are strictly convex. In this talk, I will discuss joint work with Yiran Wang which builds on the previous work by using microlocal analysis to study artifacts generated by non-convex metallic objects, as well as artifacts associated to a broader class of attenuation variations than was considered before. The problem relies on the analytic behavior of a nonlinear function composed with the image of the X-ray transform applied to certain functions, for which we use the work of Melrose, Ritter, Sa Barreto et al. on semilinear wave equations via the usage of iterated regularity spaces in which both the X-ray transform image and its nonlinear composition live.