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K-State Today

February 7, 2017

Mathematics Colloquium Lecture Feb. 7

By Reta McDermott

Dinh-Liem Nguyen, University of North Carolina at Charlotte, will present "Global Reconstruction Methods for Nonlinear Inverse Scattering Problems" as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Tuesday, Feb. 7, in 122 Cardwell Hall.

The abstract for the lecture is: In inverse scattering problems one attempts to determine geometrical and/or physical properties of the scattering medium from the measurement of the scattered wave for a number of incident waves. Applications of these problems occur in such diverse areas as nondestructive testing, geophysical exploration, medical imaging, radar or material science. Inverse scattering problems are in general highly nonlinear and ill-posed, causing substantial challenges in studying their numerical solution. Optimization-based methods are the most widely studied approach among the numerical methods for solving these inverse problems. However, these methods typically require "good" initial guesses for the solution (or detailed a priori information of the solution), which are not always available in practical applications.

In this talk, after a short introduction to inverse scattering problems, we will discuss our recent results in developing two different numerical methods for solving these problems, without using any detailed a priori information of the solution. The first method is to solve a coefficient inverse problem with a single measurement and the second one is for a shape inverse problem for periodic structures. Our numerical study was conducted on both simulated and experimental data.