Preface xiii
Introduction xv
About the Companion Website xxv
Part I Forward Scattering Problem 1
1 Scalar Waves 3
1.1 Three-Dimensional Scattering by a Bounded Contrast 5
1.1.1 Radiation in an Unbounded Homogeneous Embedding 5
1.1.2 Scattering by a Bounded Contrast 6
1.1.3 Domain-Integral Equation in the s-Domain 8
1.1.4 The Born Approximation in the s-Domain 8
1.1.5 Contrast-Source Integral Equation 9
1.2 Two-Dimensional and One-Dimensional Scattering 9
1.3 Numerical Solution of the Integral Equations (1D, 2D, 3D) 11
1.4 Matlab Input and Output Functions 17
1.5 Matlab Code for Field Integral Equations (1D, 2D, 3D) 22
1.6 Matlab Code for Contrast-Source Integral Equation 30
1.6.1 Performance Analysis 37
1.6.2 Matlab Built-in Functions for Iterative Solution of the Contrast-Source Integral Equation 41
1.7 Time-Domain Solution of Contrast-Source Integral Equation 42
1.A Representation for Homogeneous Green Functions 52
1.A.1 1D Green Function 52
1.A.2 2D Green Function 54
1.A.2.1 Cylindrical Polar Coordinates 55
1.A.3 3D Green Function 56
1.A.3.1 Spherical Polar Coordinates 58
1.B Scattering by a Simple Canonical Configuration 58
1.B.1 1D Scattering by a Slab 58
1.B.2 2D Scattering by a Circular Cylinder 60
1.B.3 3D Scattering by a Sphere 62
1.C Matlab Codes for Scattering by Canonical Objects 64
1.C.1 Matlab Code for Slab (1D) 64
1.C.2 Matlab Code for Circular Cylinder (2D) 65
1.C.3 Matlab Code for Sphere (3D) 70
1.C.4 Scattered-Field Computations Canonical Objects 76
2 Acoustic Waves 79
2.1 Three-Dimensional Scattering by a Bounded Contrast 82
2.1.1 Radiation in an Unbounded Homogeneous Embedding 82
2.1.2 Scattering by a Bounded Contrast 83
2.1.3 Contrast Source Domain Integral Equation 86
2.1.4 Numerical Solution and Operators Involved (1D, 2D, 3D) 87
2.1.4.1 Analytic Differentiation 88
2.1.4.2 Numerical Differentiation 90
2.1.4.3 Conjugate Gradient Method 92
2.1.4.4 Incident AcousticWave Field 95
2.1.4.5 Scattered AcousticWave Field 95
2.1.4.6 Weak Form of the Spatial Derivative of the Green Function 95
2.2 Matlab Codes Integral Equations: Pressure and Particle Velocity 96
2.3 Single Integral Equation in Terms of Contrast inWave Speed and Gradient of Mass Density 112
2.3.1 Contrast Source Formulation 114
2.3.2 Conjugate Gradient Iterative Solution and Operators Involved 115
2.3.2.1 Analytic Differentiation 115
2.3.2.2 Numerical Differentiation 115
2.3.2.3 Scattered AcousticWave Field 118
2.4 Matlab Codes Integral Equations:Wave Speed and Gradient of Mass Density 119
2.4.1 Performance Analysis 130
2.5 Solution of Integral Equation: Interface Contrast Sources 132
2.5.1 Contrast-Source Integral Equation 133
2.5.2 Numerical Solution of Interface Integral Equations (2D) 134
2.6 Numerical Solution Integral Equations: Volume and Interface Contrast Sources 136
2.6.1 Discrete Representations in 3D 136
2.6.2 Discrete Representations in 2D 141
2.6.3 Discrete Representations in 1D 142
2.6.4 Conjugate Gradient Iterative Solution and Operators Involved 142
2.6.4.1 Scattered AcousticWave Field 144
2.7 Matlab Codes Integral Equations: Volume and Interface Contrast Sources 147
2.7.1 Performance Analysis 158
2.7.2 Matlab BiCGSTAB Built-in Functions for Iterative Solution of the Contrast Source Integral Equation 160
2.8 Time-Domain Solution of Contrast Source Integral Equation 163
2.A Scattering by a Simple Canonical Configuration 170
2.A.1 1D Scattering by a Slab 170
2.A.2 2D Scattering by a Circular Cylinder 172
2.A.2.1 No Contrast inWave Speed 174
2.A.3 3D Scattering by a Sphere 177
2.A.4 Scattered-Field Computations Canonical Objects 179
3 Electromagnetic Waves 181
3.1 Three-Dimensional Scattering by a Bounded Contrast 184
3.1.1 Radiation in an Unbounded Homogeneous Embedding 184
3.1.2 3D Incident Electromagnetic Field 186
3.1.3 2D Incident Electromagnetic Field 187
3.1.4 Scattering by a Bounded Contrast 187
3.2 Contrast Source (E-field) Integral Equations: Permittivity Contrast Only 190
3.2.1 2D Contrast Source (E-field) Integral Equations: Permittivity Contrast Only 191
3.2.2 Conjugate Gradient Iterative Solution and Operators Involved 192
3.2.2.1 Conjugate Gradient Method 193
3.2.2.2 Scattered ElectromagneticWave Field 194
3.2.3 Matlab Codes E-field Integral Equations: Permittivity Contrast Only 195
3.2.3.1 Matlab BiCGSTAB Built-in Function 209
3.3 E-field Equation for Volume and Interface Contrast Sources: Permittivity Contrast Only 211
3.3.1 Numerical Solution with Volume and Interface Contrast Currents: Permittivity Contrast Only 214
3.3.1.1 Discrete Representations in 3D 215
3.3.1.2 Discrete Representations in 2D 219
3.3.2 Iterative Solution and Operators Involved 219
3.3.3 Matlab Codes E-field Integral Equations: Volume and Interface Contrast Sources 222
3.3.4 Performance Analysis 228
3.4 Contrast Source Integral Equations for Both Permittivity and Permeability Contrast 237
3.4.1 Numerical Solution and Operators Involved 238
3.4.1.1 Scattered ElectromagneticWave Field 240
3.4.2 Matlab Codes Integral Equations for Both Permittivity and Permeability Contrast: Special Case of ZeroWave-Speed Contrast 242
3.5 E-field Integral Equation for ZeroWave-Speed Contrast 249
3.5.1 Numerical Solution for Interface Contrast Source Integral Equation: ZeroWave-Speed Contrast 253
3.5.1.1 Discrete Representations in 3D 253
3.5.2 Matlab Codes Integral Equations for ZeroWave-Speed Contrast 256
3.6 Time-Domain Solution of Contrast Source Integral Equation 268
3.A Scattering by a Simple Canonical Configuration 279
3.A.1 2D Scattering by a Circular Cylinder 280
3.A.1.1 TM Green Function of the Circular Cylinder 280
3.A.1.2 Electromagnetic Field Strengths 282
3.A.1.3 Matlab Codes for Circular Cylinder (2D) 284
3.A.2 3D Scattering by a Sphere 292
3.A.2.1 TM Green Function of the Sphere 293
3.A.2.2 Electromagnetic Field Strengths 295
3.A.2.3 Matlab Codes for Sphere (3D) 298
3.A.3 Scattered-Field Computations Canonical Objects 306
Part II Inverse Scattering Problem 307
4 Scalar Wave Inversion 309
4.1 Notation 309
4.2 Synthetic Data 311
4.3 Nonlinear Inverse Scattering Problem 320
4.4 Inverse Contrast Source Problem 322
4.5 Contrast Source Inversion 323
4.5.1 Discretization of Green’s Operators and Norms 324
4.5.2 Updating the Contrast Sources 325
4.5.2.1 Gradient Directions 325
4.5.2.2 Calculation of the Step Length 327
4.5.3 Updating the Contrast 327
4.5.4 Initial Estimate 328
4.5.5 Matlab Codes for the CSI Method 329
4.6 Multiplicative Regularized Contrast Source Inversion 339
4.6.1 Regularization Function for the Contrast Update 339
4.6.2 Updating the Contrast with Multiplicative Regularization 341
4.6.3 Numerical Implementation of the Regularization 342
4.6.4 Numerical Solution of Regularization Equation 343
4.6.5 Matlab Codes for the MRCSI Method 344
4.7 CSI Method for Reconstruction of a Few Parameters 355
4.7.1 Gauss–Newton Method for the Contrast Update 358
4.7.2 Matlab Codes for the Gauss–Newton Type Contrast Updating 359
4.8 CSI Methods for Phaseless Data 366
4.8.1 CSI Method for Measured Intensity Data 367
4.8.2 CSI Method for Measured Amplitude Data 368
4.9 Gauss–Newton Inversion 369
4.9.1 Matlab Codes for Gauss–Newton Inversion 372
5 Acoustic Wave Inversion 377
5.1 Notation 377
5.1.1 Compressibility Contrast Only 378
5.1.2 Mass-density Contrast Only 379
5.2 Synthetic Data for Zero Compressibility Contrast 379
5.3 Mass-density Contrast Source Inversion 386
5.3.1 Updating the Contrast Sources 391
5.3.1.1 Gradient Directions 391
5.3.1.2 Calculation of the Step Length 392
5.3.2 Updating the Contrast 393
5.3.3 Initial Estimate 393
5.3.4 Updating the Contrast with Multiplicative TV Regularization 394
5.3.5 Matlab Codes for the Acoustic MRCSI Method 395
5.4 Mass-density Interface Model for ZeroWave-Speed Contrast 404
5.4.1 Synthetic Data for ZeroWave-speed Contrast 409
5.5 Mass-density Interface Contrast Source Inversion 416
5.5.1 Updating the Interface-contrast Sources 417
5.5.1.1 Gradient Directions 417
5.5.1.2 Calculation of the Step Length 418
5.5.2 Updating the Interface Contrast 418
5.5.3 Initial Estimate 419
5.5.4 Regularization by Resetting Small Interface-contrast Variation to Zero 420
5.5.5 Matlab Codes for the MICSI Method 420
5.5.6 Kirchhoff Type of Approximations 430
6 Electromagnetic Wave Inversion 439
6.1 Notation 439
6.1.1 Permittivity Contrast Only 440
6.2 Synthetic Data for Zero Permeability Contrast 441
6.3 Data Modeled with Volume and Interface Contrast Sources 453
6.4 Electromagnetic Contrast Source Inversion 459
6.4.1 Updating the Contrast Sources 460
6.4.1.1 Gradient Directions 461
6.4.1.2 Calculation of the Step Length 462
6.4.2 Updating the Contrast 462
6.4.3 Initial Estimate 463
6.4.4 Updating the Contrast with Multiplicative TV Regularization 464
6.4.5 Matlab Codes for the MRCSI Method 464
6.5 Electromagnetic Gauss–Newton Inversion 476
6.5.1 Matlab Codes for Gauss–Newton Inversion 477
6.6 Electromagnetic Defects Metrology 486
6.6.1 Data with Phase Information 490
6.6.2 Phaseless Data 493
6.6.3 Focused Data 493
Matlab Scripts 497
References 499
Biography 503
Index 505
