物理系学术报告       Physics Department Colloquium

 

31周五16:00-17:0012-201

 

 

 

Imaging via Inverse Scattering

 

Prof. Gang Bao

Department of Mathematics, Zhejiang University

 

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, near-field and nano optical imaging, and medical imaging. The model problem 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 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 problems remains to be challenging since the problems are 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 progress in mathematical analysis and computational studies of the inverse boundary value problems for the Helmholtz and Maxwell equations will be reported. Three classes of inverse scattering problems will be studied, namely inverse medium problems, inverse source problems, and inverse obstacle problems. A novel stable 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 scattering problems. Convergence issues for the continuation algorithm will be examined. The speaker will also discuss the effects of evanescent fields in achieving super-resolution via inverse scattering. Finally, he will highlight ongoing and future projects along these directions, particularly the recent work on multiscale modeling and computation of nano optics.

 

告人:

, 浙江大学数学系主任,浙江大学理学部跨学科用数学中心主任。2005年度国家杰出青年基金(B得者,2001年被聘为长江学者特聘教授。1985年吉林大学毕业1991美国莱斯(Rice)大学用数学博士学位,1991-1994先后于莱斯大学及Minnesota大学数学与用研究所博士后,1994-1999年于美国Florida大学任助理教授、副教授,1999年升任美国Michigan州立大学教授,2006创办Michigan用数学中心,2009国家千人划并于2010年初始任浙江大学教授。2003获冯康科学,曾主持美国国家科学基金、美国海科学基金、美国空科学基金30担任10个国刊物的委,包括SIAM J. Appl. Math., J. Comput. Math. Comm. Comput. Phys.。研究域:衍射光学、非线性光学、近米光学及其它波问题、偏微分方程中的反问题和最优设计问题。研究其数学建模,理分析和科学, 在国重要术杂130余篇。主持国家自然科学基金委重大科学划《高性能科学算的算法与可算建模》的重点目《复杂中波播反问题的理分析、算方法及用》