Inverse Problems and Machine Learning

Date: November 1, 2017

Time: 12:00PM - 1:00PM

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.