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

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.

Computational Methods for Electromagnetic Inverse Scattering

Xudong Chen, National University of Singapore, Singapore

This book offers a comprehensive and updated overview of the theory, algorithms and applications of electromagnetic inverse scattering problems. Fundamental theories including mathematical derivation and physical insights of both forward and inverse electromagnetic scattering will be emphasized, and 2-dimentional and 3-dimensional problems covered. Readers will be introduced to reconstruction algorithms for both small-size and large-size scatterers, as well as qualitative and quantitative reconstruction algorithms. Inverse scattering taking into account different boundary conditions are also discussed before imaging resolution and applications are tackled from a new perspective.

• Offers important advances in electromagnetic 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, Numerical Methods for Electromagnetic Inverse Scattering is an essential reference for researchers in electrical engineering, physics and applied mathematics. Graduate students and practicing engineers specializing in areas like remote sensing, military surveillance, biomedical diagnosis, nondestructive testing/evaluation, and oil exploration would also find it an insightful guide.

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

2.1.1 Representations in differential form 13

2.1.2 Time harmonic forms 14

2.1.3 Boundary conditions 15

2.1.4 Constitutive relations 16

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

2.8.1 Three-dimensional case 24

2.8.2 Two-dimensional case 27

2.8.3 Scattering by a collection of small scatterers 28

2.8.4 Degrees of freedom 28

2.9 Scattering by extended scatterers 29

2.9.1 Nonmagnetic dielectric scatterers 29

2.9.2 Perfectly electrically conducting scatterers 31

2.10 Far-field approximation 31

2.11 Reciprocity 33

2.12 Huygens? principle and extinction theorem 35

3 Time reversal imaging 41

3.1 Time reversal imaging for active sources 41

3.1.1 Explanation based on geometrical optics 41

3.1.2 Implementation steps 42

3.1.3 Fundamental theory 44

3.1.4 Analysis of resolution 48

3.1.5 Vectorial wave 49

3.2 Time reversal imaging for passive sources 51

3.2.1 Imaging by iterative time-reversal process 53

3.2.2 Imaging by the DORT method 54

3.2.3 Numerical simulations 55

3.3 Discussions 61

4 Inverse scattering problems of small scatterers 67

4.1 Forward problem: Foldy-Lax equation 68

4.2 Uniqueness theorem for inverse problem 69

4.2.1 Inverse source problem 70

4.2.2 Inverse scattering problem 71

4.3 Numerical methods 73

4.3.1 Multiple signal classification imaging 73

4.3.2 Noniterative retrieval of scattering strength 76

4.4 Inversion of vector wave equation 78

4.4.1 Forward problem 79

4.4.2 Multiple signal classification imaging 81

4.4.3 Noniterative retrieval of scattering strength tensor 88

4.4.4 Subspace imaging algorithm with enhanced resolution 90

4.5 Discussions 95

5 Linear sampling method 101

5.1 Outline of linear sampling method 102

5.2 Physical interpretation 104

5.2.1 Source distribution 104

5.2.2 Multipole radiation 106

5.3 Multipole-based linear sampling method 107

5.3.1 Description of the algorithm 107

5.3.2 Choice of the number of multipoles 108

5.3.3 Comparison with Tikhonov regularization 110

5.3.4 Numerical examples 112

5.4 Factorization method 113

5.5 Discussions 116

6 Reconstructing dielectric scatterers 119

6.1 Introduction 120

6.1.1 Uniqueness, stability, and nonlinearity 120

6.1.2 Formulation of the forward problem 122

6.1.3 Optimization approach to inverse problem 123

6.2 Noniterative inversion methods 125

6.2.1 Born approximation inversion method 125

6.2.2 Rytov approximation inversion method 126

6.2.3 Extended Born approximation inversion method 127

6.2.4 Back-propagation scheme 128

6.2.5 Numerical examples 129

6.3 Full-wave iterative inversion methods 134

6.3.1 Distorted Born iterative method 134

6.3.2 Contrast source inversion method 137

6.3.3 Contrast source extended Born method 139

6.3.4 Other iterative models 141

6.4 Subspace-based optimization method (SOM) 143

6.4.1 Gs-SOM 144