PDE Seminar

Title: Streak artifacts from non-convex metal objects in X-ray tomography
Speaker: Yuzhou (Joey) Zou
Speaker Info: Northwestern University
Brief Description:
Special Note:

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 was given by Choi, Park, and Seo in 2014 using the notion of wavefront sets, 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 using the machinery of (paired) Lagrangian distributions. In this talk, I will discuss joint work with Yiran Wang which studies artifacts generated by non-convex metallic objects, as well as "finite iterated regularity" artifacts which were not considered previously. 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.
Date: Thursday, April 13, 2023
Time: 12pm
Where: Lunt 107
Contact Person: Ruoyu Wang
Contact email: rptwang@math.northwestern.edu
Contact Phone: 2243075512
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