Numerical Methods for Inverse Scattering Problems

This book highlights the latest developments on the numerical methods for inverse scattering problems associated with acoustic, electromagnetic, and elastic waves. Inverse scattering problems are concerned with identifying unknown or inaccessible objects by wave probing data, which makes possible many industrial and engineering applications including radar and sonar, medical imaging, nondestructive testing, remote sensing, and geophysical exploration. The mathematical study of inverse scattering problems is an active field of research. This book presents a comprehensive and unified mathematical treatment of various inverse scattering problems mainly from a numerical reconstruction perspective. It highlights the collaborative research outputs by the two groups of the authors yet surveys and reviews many existing results by global researchers in the literature. The book consists of three parts respectively corresponding to the studies on acoustic, electromagnetic, and elastic scattering problems. In each part, the authors start with in-depth theoretical and computational treatments of the forward scattering problems and then discuss various numerical reconstruction schemes for the associated inverse scattering problems in different scenarios of practical interest. In addition, the authors provide an overview of the existing results in the literature by other researchers. This book can serve as a handy reference for researchers or practitioners who are working on or implementing inverse scattering methods. It can also serve as a graduate textbook for research students who are interested in working on numerical algorithms for inverse scattering problems.

Jingzhi LI is a professor at Department of Mathematics, Southern University of Science and Technology (SUSTech), China. He completed his Ph.D. study in Applied Mathematics in 2009 from the Chinese University of Hong Kong. His Ph.D. research was awarded Best Dissertation Award by the Mathematical Society of Hong Kong in 2011. Then, he spent two years working in the Department of Mathematics, ETH Zurich, Switzerland, as postdoctoral fellow. In 2011, he took an assistant professor position at Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences (CAS). In early 2012, he was enlisted in the Thousand Young Talents Recruitment Program of the Chinese government, top tier global recruitment program for young overseas scholars, and acquired early-career funding. He joined SUSTech in 2012 and served as an associate professor and then a full professor. 

Hongyu LIU is a professor of Mathematics at the City University of Hong Kong, China. He obtained his Ph.D. in Mathematics from The Chinese University of Hong Kong in 2007. Before taking up the current position, he held faculty positions in Hong Kong Baptist University, the University of North Carolina at Charlotte in USA, the University of Reading in UK, and the University of Washington at Seattle in the USA. His research interests include inverse problems for partial differential equations, wave propagations, mathematical materials science, scattering theory, spectral theory, scientific computing, and machine learning. His research recognitions include the Calderon Prize by the Inverse Problems International Association, a Changjiang Chair Professorship by the Ministry of Education of China, and Hong Kong Mathematical Society Young Scholar Award.