Numerical Methods for Inverse Scattering Problems

✍ Scribed by Jingzhi Li, Hongyu Liu

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 373
• Category: Library

✦ Synopsis

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 scatteringproblems. 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.

✦ Table of Contents

Preface
Acknowledgements
Contents
1 Introduction
References
2 Direct Acoustic Scattering Problems
2.1 Acoustic Scattering From Obstacles
2.2 Acoustic Scattering From Mediums
2.3 Acoustic Scattering From Complex Scatterers
2.4 Green's Formula and Linear Potential Theory for Scattering Problems
2.5 Numerical Methods for Acoustic Scattering Problems
2.5.1 Nyström Method
2.5.2 Finite Element Method with Perfectly Matched Layer (PML)
References
3 Numerical Inverse Acoustic Scattering Problems
3.1 Overview
3.2 Strengthened Linear Sampling Methods
3.2.1 Strengthened Linear Sampling Method with a Reference Ball
3.2.2 Numerical Experiments and Discussion
3.2.3 Conclusion
3.3 Single-Shot Method for Multiple Multiscale Scatterers
3.3.1 Locating Small Scatterers
3.3.2 Locating Scatterers of Regular Size
3.3.3 Locating Scatterers of Multiple Scales
3.4 Reconstruction by Phaseless Backscattering Measurements
3.4.1 Physical Optics Approximation
3.4.2 Recovery Scheme
3.4.3 Numerical Experiments and Discussions
3.4.4 Concluding Remarks
References
4 Direct Electromagnetic Scattering Problems
4.1 Electromagnetic Scattering From Obstacles
4.2 Electromagnetic Scattering From Mediums
4.3 Electromagnetic Scattering From Complex Scatterers
4.4 Green's Theorem and Representation Formulas
4.5 Numerical Methods for Electromagnetic Scattering Problems
References
5 Numerical Inverse Electromagnetic Scattering Problems
5.1 Overview
5.2 Strengthened Linear Sampling Methods
5.3 Single-shot Method for Multiple Multiscale Scatterers
5.3.1 The Locating Schemes
5.3.2 Proofs of Theorems 5.3.1 and 5.3.2
5.3.3 Numerical Experiments and Discussions
5.3.4 Concluding Remarks
5.4 Scatterers
5.4.1 Multi-scale EM Scatterers and Two Locating Schemes
5.4.2 Scheme R with Augmented Reference Spaces
5.4.3 Locating Multiple Multi-scale Scatterers
5.4.4 Numerical Experiments and Discussions
5.4.5 Discussions
References
6 Direct Elastic Scattering Problems
6.1 Elastic Scattering from Obstacles
6.2 Elastic Scattering from Mediums
6.3 Elastic Scattering from Complex Scatterers
6.4 Green's Theorems and Representation Formulas
6.5 Numerical Methods for Elastic Scattering Problems
References
7 Numerical Inverse Elastic Scattering Problems
7.1 Overview
7.2 Single-Shot Method for Multiple Multiscale Scatterers
7.2.1 Locating Multiple Small Scatterers
7.2.2 Locating Multiple Extended Scatterers
7.2.3 Locating Multiple Multiscale Scatterers
7.2.4 Numerical Examples
7.2.5 Concluding Remarks
7.3 Traction Free Case
7.3.1 Elastic Scattering From Multiscale Scatterers
7.3.2 Locating Multiple Multiscale Elastic Scatterers
7.4 Reconstructing Multiple Small Scatterers
7.5 Reconstructing Multiple Extended Scatterers
7.6 Reconstructing Multiple Multiscale Scatterers
7.7 Two-Stage Fast Imaging of Multiple Multiscale Scatterers
References
8 Miscellaneous Topics
8.1 Multilevel Linear Sampling Methods
8.1.1 Multilevel Linear Sampling Method
8.1.2 Numerical Experiments and Some Discussions
8.2 EMLSM
8.2.1 Inverse Acoustic Obstacle Scattering Problem
8.2.2 Review of LSM and MLSM
8.2.3 Enhanced Multilevel-LSMs
8.2.4 Numerical Experiments
References
9 Others
9.1 Ground Detection by a Single Electromagnetic Far-Field Measurement
9.1.1 Scattering from Multiscale Ground Objects
9.1.2 Locating Multiscale Ground Objects
9.1.3 Numerical Experiments and Discussions
9.2 Recovering Multiscale Buried Anomalies in a Two-Layered Medium
9.2.1 Mathematical Formulation
9.2.2 Results on Direct Scattering Problem
9.2.3 Recovery Scheme
9.2.4 Numerical Experiments
References