Electromagnetic Inverse Scatte

1. Auflage 2018
ISBN: 978-1-119-31198-0
Verlag: Wiley

Buch, Englisch, 328 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 626 g

A comprehensive and updated overview of the theory, algorithms and applications of for electromagnetic inverse scattering problems
- Offers the recent and most important advances in inverse scattering grounded in fundamental theory, algorithms and practical engineering applications
- Covers the latest, most relevant inverse scattering techniques like signal subspace methods, time reversal, linear sampling, qualitative methods, compressive sensing, and noniterative methods
- Emphasizes theory, mathematical derivation and physical insights of various inverse scattering problems
- Written by a leading expert in the field

Autoren/Hrsg.

Chen, Xudong

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik
• Technische Wissenschaften Energietechnik | Elektrotechnik Elektrotechnik

Inhaltsverzeichnis

Foreword xiii
Preface xv

1 Introduction 1
1.1 Introduction to Electromagnetic Inverse Scattering Problems 1
1.2 Forward Scattering Problems 2
1.3 Properties of Inverse Scattering Problems 3
1.4 Scope of the Book 6

2 Fundamentals of Electromagnetic Wave Theory 13
2.1 Maxwell's Equations 13
2.2 General Description of a Scattering Problem 16
2.3 Duality Principle 18
2.4 Radiation in Free Space 18
2.5 Volume Integral Equations for Dielectric Scatterers 20
2.6 Surface Integral Equations for Perfectly Conducting Scatterers 21
2.7 Two-Dimensional Scattering Problems 22
2.8 Scattering by Small Scatterers 24
2.9 Scattering by Extended Scatterers 29
2.10 Far-Field Approximation 32
2.11 Reciprocity 34
2.12 Huygens' Principle and Extinction Theorem 35

3 Time-Reversal Imaging 41
3.1 Time-Reversal Imaging for Active Sources 41
3.2 Time-Reversal Imaging for Passive Sources 53
3.3 Discussions 62

4 Inverse Scattering Problems of Small Scatterers 67
4.1 Forward Problem: Foldy–Lax Equation 68
4.2 Uniqueness Theorem for the Inverse Problem 69
4.3 Numerical Methods 73
4.4 Inversion of a Vector Wave Equation 79
4.5 Discussions 97

5 Linear Sampling Method 103
5.1 Outline of the Linear Sampling Method 104
5.2 Physical Interpretation 106
5.3 Multipole-Based Linear Sampling Method 109
5.4 Factorization Method 116
5.5 Discussions 118

6 Reconstructing Dielectric Scatterers 123
6.1 Introduction 124
6.2 Noniterative Inversion Methods 129
6.3 Full-Wave Iterative Inversion Methods 139
6.4 Subspace-Based Optimization Method (SOM) 149
6.5 Discussions 171

7 Reconstructing Perfect Electric Conductors 183
7.1 Introduction 183
7.2 Inversion Models Requiring Prior Information 185
7.3 Inversion Models Without Prior Information 186
7.4 Mixture of PEC and Dielectric Scatterers 196
7.5 Discussions 202

8 Inversion for Phaseless Data 207
8.1 Introduction 207
8.2 Reconstructing Point-Like Scatterers by Subspace Methods 209
8.3 Reconstructing Point-Like Scatterers by Compressive Sensing 214
8.4 Reconstructing Extended Dielectric Scatterers 220
8.5 Discussions 223

9 Inversion with an Inhomogeneous Background Medium 227
9.1 Introduction 227
9.2 Integral Equation Approach via Numerical Green's Function 229
9.3 Differential Equation Approach 235
9.4 Homogeneous Background Approach 240
9.5 Examples of Three-Dimensional Problems 243
9.6 Discussions 252

10 Resolution of Computational Imaging 257
10.1 Diffraction-Limited Imaging System 257
10.2 Computational Imaging 261
10.3 Cramér–Rao Bound 264
10.4 Resolution under the Born Approximation 268
10.5 Discussions 272
10.6 Summary 277
References 278

Appendices A Ill-Posed Problems and Regularization 281
A. 1 Ill-Posed Problems 281
A. 2 Regularization Theory 282
A. 3 Regularization Schemes 283
A. 4 Regularization Parameter Selection Methods 286
A. 5 Discussions 288

B Least Squares 291
B.1 Geometric Interpretation of Least Squares 291
B.2 Gradient of Squared Residuals 292

C conjugate Gradient Method 295
C.1 Solving General Minimization Problems 295
C.2 Solving Linear Equation Systems 296

D Matrix-Vector Product by the FFT Procedure 299
D. 1 One-Dimensional Case 299
D. 2 Two-Dimensional Case 300

Appendix References 301
Index 303

Über Autor(innen)

Xudong Chen, received the B.S. and M.S. degrees in electrical engineering from Zhejiang University, Hangzhou, China, in 1999 and 2001, respectively, and the Ph.D. degree from the Massachusetts Institute of Technology, Cambridge, MA, USA, in 2005. Since then he joined the Department of Electrical and Computer Engineering, National University of Singapore, Singapore, and he is currently an Associate Professor. His research interests include mainly electromagnetic inverse problems. He has published more than 120 peer-reviewed journal papers on inverse scattering problems, material parameter retrieval, and optical encryption. The total citation of his papers is about 2,500 according to ISI Web of Science till Dec 2015. He visited the University of Paris-SUD 11 in May-June 2010 as an invited visiting Associate Professor. He was the recipient of the Young Scientist Award by the Union Radio-Scientifique Internationale (URSI) in 2010 and Engineering Young Researcher Award by FOE, National University of Singapore in 2015. He is currently an Associate Editor of the IEEE Transactions on Microwave Theory and Techniques.