Polarimetric Scattering and Sar Information Retrieval

Ya-Qiu Jin, Fudan University, China
Professor Jin is Chair Professor and Director of the Key Lab of Wave Scattering and Remote Sensing Information, at Fudan University, Shanghai, China. He is an IEEE Fellow, a Fellow of the Electromagnetics Academy (USA) and CIE as well as being Chair of the IEEE Fellow Evaluation Committee (GRSS), a Member of IEEE GRSS AdCom, and Associate Editor of IEEE Transactions on Geoscience and Remote Sensing.

Feng Xu, Intelligent Automation, Inc, USA
Dr. Xu holds the post of Research Scientist at Intelligent Automation, Inc, Rockville, USA. He took his PhD at Fudan University in Shanghai, China and was a postdoctoral researcher at NOAA/NESDIS, USA, from 2008-2009.

Preface xi

1 Basics of Polarimetric Scattering 1

1.1 Polarized Electromagnetic Wave 1

1.1.1 Jones Vector and Scattering Matrix 1

1.1.2 Stokes Vector and Mueller Matrix 4

1.2 Volumetric Scattering 9

1.2.1 Small Particle under Rayleigh–Gans Approximation 9

1.2.2 Slim Cylinder 11

1.3 Surface Scattering 13

1.3.1 Plane Surface 13

1.3.2 Rough Surface 14

1.3.3 Kirchhoff Approximation 16

1.3.4 Small-Perturbation Approximation 19

1.3.5 Two-Scale Approximation 21

1.3.6 Integral Equation Method 22

1.3.7 Tilted Surface or Oriented Object 25

References 26

2 Vector Radiative Transfer 29

2.1 Radiative Transfer Equation 29

2.1.1 Specific Intensity and Stokes Vector 29

2.1.2 Thermal Emission and Brightness Temperature 32

2.1.3 Vector Radiative Transfer Equation 33

2.2 Components in Radiative Transfer Equation 35

2.2.1 Scattering, Absorption, and Extinction Coefficients 35

2.2.2 Extinction Matrix 36

2.2.3 Phase Matrix 39

2.3 Mueller Matrix Solution 40

2.3.1 First-Order Mueller Matrix Solution 40

2.3.2 Modeling of Vegetation Canopy over Rough Surface 43

2.3.3 Numerical Examples of Modeling of Vegetation Canopy 47

2.4 Polarization Indices and Entropy 52

2.4.1 Eigen-Analysis of Mueller Matrix 52

2.4.2 Relationship between Eigenvalues, Entropy, and Polarization Indices 53

2.4.3 Demonstration with AirSAR Imagery 55

2.5 Statistics of Stokes Parameters 59

2.5.1 Multi-Look Covariance Matrix and Complex Wishart Distribution 59

2.5.2 PDFs of the Four Stokes Parameters 60

2.5.3 Comparison with AirSAR Image Data 67

Appendix 2A: Phase Matrix of Non-Spherical Particles 72

References 76

3 Imaging Simulation of Polarimetric SAR: Mapping and Projection Algorithm 79

3.1 Fundamentals of SAR Imaging 79

3.1.1 Ranging and Pulse Compression 79

3.1.2 Synthetic Aperture and Azimuth Focusing 82

3.1.3 SAR Imaging Algorithm 85

3.2 Mapping and Projection Algorithm 90

3.2.1 Mapping and Projection 91

3.2.2 Mapping and Projection Algorithm for Fast Computation 95

3.2.3 Scattering Models for Terrain Objects 101

3.2.4 Speckle Model and Raw Data Generation 105

3.3 Platform for SAR Simulation 108

3.3.1 Simulation of Individual Terrain Objects 108

3.3.2 Simulation of Comprehensive Terrain Scene 112

3.3.3 Extensions 119

References 121

4 Bistatic SAR: Simulation, Processing, and Interpretation 123

4.1 Bistatic Mapping and Projection Algorithm (BI-MPA) 124

4.1.1 Configurations of BISAR 124

4.1.2 Three-Dimensional Projection and Mapping 125

4.1.3 Multiple Scattering Terms 130

4.2 Scattering Models and Signal Model 130

4.2.1 Models of Terrain Objects 130

4.2.2 Raw Signal Model for BISAR 131

4.3 Simulated BISAR Images 136

4.4 Polarimetric Characteristics of BISAR Image 141

4.5 Unified Bistatic Polarization Bases 146

4.6 Raw Signal Processing of Stripmap BISAR 150

4.6.1 Approximate Form of the Point Target Response 150

4.6.2 Validity Condition and an Iterative Solution 155

4.6.3 Extension of Range Doppler Method 157

4.6.4 Simulation and Discussion 159

References 164

5 Radar Polarimetry and Deorientation Theory 167

5.1 Radar Polarimetry and Target Decomposition 167

5.1.1 Polarization Transformation 167

5.1.2 Radar Polarimetry 173

5.1.3 Target Decomposition 180

5.2 Deorientation Theory 184

5.2.1 Deorientation 184

5.2.2 Efficacy of Deorientation 192

5.3 Terrain Surface Classification 198

5.3.1 Terrain Scattering Modeling and Classification Spectrum 198

5.3.2 Application to SIR-C Data 201

5.3.3 Orientation Analysis 206

Appendix 5A: Matrix Transformations under Various Conventions 207

5A.1 Transformation under Wave Coordinates (FSA) 209

5A.2 Transformation under Antenna Coordinates (BSA) 211

5A.3 Interconversion between Wave Coordinates (FSA) and Antenna

Coordinates (BSA) 213

References 213

6 Inversions from Polarimetric SAR Images 215

6.1 Inversion of Digital Elevation Mapping 216

6.1.1 The Shift of Orientation Angle 216

6.1.2 Range and Azimuth Angles from Euler Angle Transformation 218

6.1.3 The Azimuth Angle of Every Pixel in a SAR Image 220

6.2 An Example of Algorithm Implementation 221

6.3 Inversion of Bridge Height 225

6.3.1 Geometric Rays Projection for Analysis of Bridge Scattering 225

6.3.2 SAR Image Simulation of a Bridge Object 226

6.3.3 Inversion of Naruto Bridge Height using Classification Parameters 227

6.3.4 Inversion of the Height of Eastern Sea Bridge using ALOS SAR Data 231

References 233

7 Automatic Reconstruction of Building Objects from Multi-Aspect SAR Images 235

7.1 Detection and Extraction of Object Image 237

7.1.1 Features of a Simple Building Object in a SAR Image with Meter Resolution 237

7.1.2 CFAR Edge Detection and Ridge Filter Thinning 238

7.1.3 Building Image Extraction via Hough Transform 242

7.1.4 Classification of Building Images 246

7.2 Building Reconstruction from a Multi-Aspect Image 247

7.2.1 Probabilistic Description of Building Image 247

7.2.2 Multi-Aspect Coherence of Building Images 250

7.2.3 Multi-Aspect Co-Registration 255

7.3 Automatic Multi-Aspect Reconstruction (AMAR) 257

7.4 Results and Discussion 260

7.4.1 Analysis of Reconstruction Results 260

7.4.2 Discussion 264

7.5 Calibration and Validation of Multi-Aspect SAR Data 265

7.5.1 Method 265

7.5.2 Experiments 268

References 273

8 Faraday Rotation on Polarimetric SAR Image at UHF/VHF Bands 275

8.1 Faraday Rotation Effect on Terrain Surface Classification 276

8.1.1 Faraday Rotation in Plasma Media 276

8.1.2 Mueller Matrix with Faraday Rotation 278

8.2 Recovering the Mueller Matrix with Ambiguity Error p/2 283

8.3 Method to Eliminate the p/2 Ambiguity Error 287

References 290

9 Change Detection from Multi-Temporal SAR Images 291

9.1 The 2EM-MRF Algorithm 292

9.1.1 The EM Algorithm 292

9.1.2 Two-Thresholds EM Algorithm 293

9.1.3 Spatial–Textual Classification based on MRF 295

9.2 The 2EM-MRF for Change Detection in an Urban Area 298

9.3 Change Detection after the 2008 Wenchuan Earthquake 301

References 308

10 Temporal Mueller Matrix for Polarimetric Scattering 311

10.1 Radiative Transfer in Inhomogeneous Random Scattering Media 312

10.2 Time-Dependent Mueller Matrix for Inhomogeneous Random Media 317

10.3 Polarimetric Bistatic and Backscattering Pulse Responses 321

10.4 Pulse Echoes from Lunar Regolith Layer 328

10.4.1 Mueller Matrix Solution for Seven Scattering Mechanisms 329

10.4.2 Numerical Simulation of Pulse Echoes 333

10.4.3 Pulse Echo Images of Lunar Layered Media 336

10.5 Monitoring Debris and Landslides 339

10.5.1 Modeling Debris Flows and Landslides 340

10.5.2 Echo Simulation of Nadir Looking Radar 342

Appendix 10A: Some Mathematics Needed in Derivation of Temporal Mueller Matrix 346

References 348

11 Fast Computation of Composite Scattering from an Electrically Large Target over a Randomly Rough Surface 351

11.1 Bidirectional Analytic Ray Tracing 352

11.1.1 Bidirectional Tracing 352

11.1.2 Analytic Tracing 356

11.1.3 Rough Facets 360

11.2 Numerical Results 361

References 374

12 Reconstruction of a 3D Complex Target using Downward-Looking Step-Frequency Radar 375

12.1 Principle of 3D Reconstruction 376

12.1.1 Principle of Imaging based on Point Scattering 376

12.1.2 Imaging Algorithm using 3D Fast Fourier Transform 379

12.1.3 Resolution and Sampling Criteria 382

12.2 Scattering Simulation and 3D Reconstruction 382

12.2.1 Model of Square Frustum (Case I) 383

12.2.2 Model of Tank-Like Target (Case II) 386

12.2.3 Tank-Like Model over Rough Surface (Case III) 388

References 392

Index 395

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