Back to Departmental Colloquium: Spring 2009
Departmental Colloquium
Date: Thursday, Apr 9, 2009
Time: 4:15PM
Location: JWB 335
Gang Bao
Michigan State
Title |
Distinguishability via Uncertainty Principle for inverse Scattering |
Abstract |
The inverse scattering problem arises in diverse areas of industrial and military applications, such as nondestructive testing, seismic imaging, submarine detections, near-field or subsurface imaging, and medical imaging. A general model is concerned with a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain. Given the incident field, the direct problem is to determine the scattered field for the known scatterer. The inverse medium scattering problem is to determine the scatterer from the boundary measurements of near field currents densities. Although this is a classical problem in mathematical physics, numerical solution of the inverse problem remains to be challenging since the problem is nonlinear, large-scale, and most of all ill-posed! The severe ill-posedness has thus far limited in many ways the scope of inverse problem methods in practical applications. In this talk, our recent results in mathematical analysis and computational studies of the inverse boundary value problems for the Maxwell equations will be reported. A novel continuation approach based on the uncertainty principle will be presented. By using multi-frequency or multi-spatial frequency boundary data, our approach is shown to overcome the ill-posedness for the inverse medium scattering problems. Convergence issues for the continuation algorithm will be examined. Our most recent progress on inverse source problems will also be discussed. |
Mathematical Biology
Computational Mathematics