Weimin Han

University of Iowa

Weimin Han is the recipient of a 21012 Simons Fellowship in Mathematics. This fall, he is working on “Mathematical Problems in X-ray Dark-field Tomography,” a project focusing on mathematical analysis and numerical solution of problems arising in x-ray dark-field tomography (XDT) for x-ray imaging through contrast mechanism in terms of scattering. Proposed research topics include well-posedness of a new system of partial differential equations, uniqueness results for the related inverse problem of reconstructing the scattering coefficient, convergence and error analysis for numerical methods in solving the problems, theoretical and numerical comparisons for different choices of the regularization term employed in numerically solving the XDT problem, and implementation of numerical methods and illustrations through numerical examples. These research topics are not only challenging academically but also important in application in medical sciences.