β Scribed by Fioralba Cakoni, David Colton, Peter Monk
No coin nor oath required. For personal study only.
The linear sampling method is the oldest and most developed of the qualitative methods in inverse scattering theory. It is based on solving a linear integral equation and then using the equation s solution as an indicator function for the determination of the support of the scattering object. This book describes the linear sampling method for a variety of electromagnetic scattering problems. It presents uniqueness theorems and the derivation of various inequalities on the material properties of the scattering object from a knowledge of the far field pattern of the scattered wave. Also covered are the approximation properties of Herglotz wave functions; the behavior of solutions to the interior transmission problem, a novel interior boundary value problem; and numerical examples of the inversion scheme. Audience: This book is intended for mathematicians and engineers performing research in inverse electromagnetic scattering theory. It is also appropriate for an advanced graduate course on inverse problems. Contents: Preface; Chapter 1: Inverse Scattering in Two Dimensions; Chapter 2: Maxwell s Equations; Chapter 3: The Inverse Problem for Obstacles; Chapter 4: The Inverse Scattering Problem for Anisotropic Media; Chapter 5: The Inverse Scattering Problem for Thin Objects; Chapter 6: The Inverse Scattering Problem for Buried Objects; Bibliography; Index.
Contents......Page 7
Preface......Page 9
1.1 Introduction......Page 11
1.2 Classical Inversion Techniques......Page 14
1.3 The Linear Sampling Method......Page 17
1.4 Regularization of the LSM......Page 19
1.5 Numerical Results in Two Dimensions......Page 21
2.1 The Scattering of Electromagnetic Waves......Page 29
2.2 The StrattonβChu Formulae and Their Application......Page 31
2.3 Vector Wave Functions and Electromagnetic Herglotz Pairs......Page 35
3 The Inverse Scattering Problem for Obstacles......Page 38
3.1 A Uniqueness Theorem......Page 39
3.2 Approximation Properties of Electromagnetic Herglotz Pairs......Page 41
3.3 The Linear Sampling Method......Page 47
3.4 Limited Aperture Data......Page 54
3.5 Numerical Examples in Three Dimensions......Page 55
4 The Inverse Scattering Problem for Anisotropic Media......Page 62
4.1 Uniqueness Theorems......Page 64
4.2 The Interior Transmission Problem......Page 78
4.3 Determination of the Support......Page 85
4.4 A Lower Bound for......Page 89
4.5 The Existence of Transmission Eigenvalues......Page 92
4.6 Partially Coated Objects......Page 98
5.1 Scattering by Thin Objects......Page 102
5.2 Approximation Theorems......Page 106
5.3 Solution of the Inverse Problem......Page 108
5.4 Numerical Reconstruction of Screens......Page 114
6 The Inverse Scattering Problem for Buried Objects......Page 116
6.1 Scattering by Buried Objects......Page 117
6.2 Near Field Data......Page 119
6.3 The Reciprocity Gap Functional Method......Page 121
6.4 Numerical Reconstruction of Buried Objects......Page 135
Bibliography......Page 138
Index......Page 146
π SIMILAR VOLUMES
Draws together some mathematical ideas that are useful in population genetics, concentrating on a few aspects which are both biologically relevant and mathematically interesting.
Draws together some mathematical ideas that are useful in population genetics, concentrating on a few aspects which are both biologically relevant and mathematically interesting.
Draws together some mathematical ideas that are useful in population genetics, concentrating on a few aspects which are both biologically relevant and mathematically interesting.
Addresses external biofluiddynamics concerning animal locomotion through surrounding fluid media - and internal biofluiddynamics concerning heat and mass transport by fluid flow systems within an animal.