ECE Seminar Series

Joint Electrical and Computer Engineering, Computer Science, and Inverse Problems Seminar

Title: Regularization of the Inverse Scattering Problem using Shearlet Frames
Speaker: Gitta Kutyniok
Affiliation: Technical University of Berlin
Day: Thursday, February 5, 2015
Time: 2:00 pm - 3:00 pm
Location: LSC 322

Abstract: The scattering problem analyzes how incident waves, radiation, or particles, which are transmitted in a medium, are scattered at inhomogeneities of this medium. The associated inverse problem aims to determine characteristics of the inhomogeneities from the asymptotic behavior of such scattered waves. This problem appears in various flavors in different application areas, e.g. non-destructive testing, ultrasound tomography, and echolocation. In this talk, our focus will be on regularization techniques for the numerical solution of inverse scattering problems in two space dimensions. Assuming that the boundary of a scatterer is its most prominent feature, we exploit as model the class of cartoon-like functions. Since functions in this class are asymptotically optimally sparsely approximated by shearlet frames, we consider shearlets as a means for regularization. We then analyze two approaches, namely the nonlinear problem and a linearized problem obtained by the Born approximation technique. For the first class, we study the acoustic inverse scattering problem, whereas for the second class, we consider the inverse scattering problem of the Schrodinger equation. Besides a theoretical analysis of our numerical approaches, we will also provide numerical examples that highlight the effectiveness of our schemes. This is joint work with Volker Mehrmann and Philipp Petersen (TU Berlin).

Bio: Gitta Kutyniok completed her Diploma in Mathematics and Computer Science in 1996 at the Universitat Paderborn in Germany. She received her Ph.D. degree in the area of time-frequency analysis from the same university in 2000. She completed her Habilitation in Mathematics in 2006 and received her venia legendi. In 2007, she was awarded a Heisenberg Fellowship by the DFG-German Research Foundation. From 2001 to 2008 she held visiting appointments at several US institutions, including Princeton University, Stanford University, Yale University, Georgia Institute of Technology, and Washington University in St. Louis. After returning to Germany in October 2008, she became a full professor of mathematics at the Universitat Osnabrueck, and headed the Applied Analysis Group. Since October 2011, she has an Einstein Chair at the Technical University of Berlin and is head of the Applied Functional Analysis Group (AFG). Her research and teaching have been recognized by various awards, including the von Kaven Prize by the German Research Foundation, awards by the University Paderborn and the Justus-Liebig University Giessen for Excellence in Research, as well as the Weierstrass Prize for Outstanding Teaching. She will also deliver the Noether-Lecture at this year's annual meeting of the Mathematical Societies from Germany and Austria. She is an Associate Editor and also Corresponding Editor for several journals in the area of applied mathematics. She is also a board member of the Berlin Mathematical School, a member of the council of the MATHEON "Mathematics for key technologies" in Berlin, and the chair of the GAMM activity group on "Mathematical Signal- and Image Processing".