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Inverse Problems Seminar

Fall 2017

Date:November 1, 2017
Location:BLOC 628
Speaker:Dr. Vitaly Katsnelson, Rice University, Applied Math DEpartment
Title:Reconstruction of a piecewise smooth wave speed from exterior measurements
Abstract:We will discuss how to reconstruct a piecewise smooth wave speed inside a domain D with boundary using only measurements taken outside of D; such measurements are akin to having a hyperbolic Neumann-to-Dirichlet map as one's given data. The main obstacle is the internal multiple scattering occurring within D due to the interfaces. We will show how to control and eliminate these internal multiples to eventually reconstruct the location of the interfaces and the wave speed itself. Our methods work for the local inverse problem as well. Numerical simulations will also be presented.

Date:December 1, 2017
Location:BLOC 628
Speaker: Mahmood Ettehad, Texas A&M University
Title:Network graph reconstruction from path correlations (Joint with Math Physics and Harmonic Analysis seminar))

Date:December 6, 2017
Location:BLOC 628
Speaker:Dr. Matthew Lewis, UT Southwest Medical Center, Radiology Department
Title:Secrets of Spectral Computed Tomography
Abstract: In the past ten years, all three major vendors of clinical CT have released different kinds of CT systems that exploit the energy-dependence of X-ray attenuation. In this talk, I will discuss the dimensionality of X-ray contrast and how these different CT systems work. Examples of artifacts of unknown origin will be presented and related to model non-linearities. Model errors due to K-edges will also be presented, with a question to applied mathematicians: how can we exploit these singularities in novel ways? Lastly, I will conclude with a discussion of next generation photon-counting spectral CT.