Table of contents for Qualitative methods in inverse scattering theory : an introduction / Fioralba Cakoni, David Colton.

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1   Functional Analysis and Sobolev Spaces ................... 1
1.1  Normed  Spaces .........................................  1
1.2  Bounded  Linear Operators .  ............................ ..  6
1.3 The Adjoint Operator................................    13
1.4 The Sobolev Space HP[0, 27r] .. . ........................   17
1.5 The Sobolev Space HP(OD) .............................. 22
2   Ill-Posed  Problem s  ....................... .............  .  27
2.1 Regularization Methods . ............................... 28
2.2  Singular Value Decomposition.....................  ... .. .  30
2.3  Tikhonov  Regularization  .............................. ..  36
3   Scattering by an Imperfect Conductor ..................... 45
3.1 Maxwell's Equations .............. ..................... 45
3.2 Bessel Functions. ................  ..................... 47
3.3  The Direct Scattering  Problem  ......................... . .  51
4   The Inverse Scattering Problem
for an Imperfect Conductor .............. ............... . 61
4.1  Far Field  Patterns.......................... ..........  62
4.2 Uniqueness Theorems for the Inverse Problem............... 65
4.3  The Linear Sampling Method  ..........................  .  69
4.4 Determination of the Surface Impedance ................. . 76
4.5 Limited Aperture Data . .............................. . 79
5   Scattering by an Orthotropic Medium ................... . 81
5.1 Maxwell Equations for an Orthotropic Medium............ . 81
5.2 Mathematical Formulation
of the Direct Scattering Problem  ........................  .  85
5.3  Variational Methods  ................. .... .............  89
5.4 Solution of the Direct Scattering Problem ................ .101
6   The Inverse Scattering Problem
for an Orthotropic Medium............................ 105
6.1  Formulation  of the Inverse Problem  ................... ....  105
6.2  The Interior Transmission  Problem  .................. ....  108
6.3 Uniqueness ............................................. 117
6.4 The Linear Sampling Method ........................... 120
7   The  Factorization  M ethod  ...................  ..........  131
7.1 Preliminary Results ............. . ..................... 132
7.2  Properties of the Far Field  Operator ...................... 1412
7.3 The Factorization Method .............................146
7.4 Closing Remarks ...................................151
8   Mixed Boundary Value Problems ......................... 153
8.1 Scattering by a Partially Coated Perfect Conductor ......... 154
8.2 The Inverse Scattering Problem for a Partially Coated
Perfect Conductor ................................... 161
8.3 Numerical Examples .................................. 166
8.4 Scattering by a Partially Coated Dielectric................. 171
8.5 The Inverse Scattering Problem
for a  Partially  Coated  Dielectric ........................ .  180
8.6 Numerical Examples .................................. 188
8.7 Scattering by Cracks .................................. 192
8.8 The Inverse Scattering Problem for Cracks ................. 201
8.9 Numerical Examples ..................................209
9   A Glimpse at Maxwell's Equations ........................ 213
References ...................................................219
Index  ............  ............................. ...............225