# SAR Image Analysis - A Computational Statistics Approach

## With R Code, Data, and Applications

1. Edition October 2022

208 Pages, Hardcover*Wiley & Sons Ltd*

**978-1-119-79529-2**

SAR IMAGE ANALYSIS -- A COMPUTATIONAL STATISTICS APPROACH

Discover how to use statistics to extract information from SAR imagery

In SAR Image Analysis -- A Computational Statistics Approach, an accomplished team of researchers delivers a practical exploration of how to use statistics to extract information from SAR imagery. The authors discuss various models, supply sample data and code, and explain theoretical aspects of SAR image analysis that are highly relevant to practitioners and students.

The book offers the theoretical properties of models, estimators, interpretation, data visualization, and advanced techniques, along with the data and code samples, that students require to learn effectively and efficiently.

SAR Image Analysis -- A Computational Statistics Approach provides various exercises throughout the book to help readers reinforce and retain the extensive information on parameter estimation, applications, reproducibility, replicability, and advanced topics, like robust estimators and stochastic distances, contained within.

The book also includes:

* Thorough introductions to data acquisition and the elements of data analysis and image processing with R, including useful R packages, preprocessing SAR data, and visualization

* Comprehensive explorations of intensity SAR data and the multiplicative model, including the (SAR) gamma distribution, the K distribution, the G° distribution, and more general distributions under the multiplicative model

* Practical discussions of parameter estimations, including the Bernoulli distribution, the negative binomial distribution, and the uniform distribution

* In-depth examinations of applications, including statistical filters and classification

Perfect for undergraduate and graduate students studying remote sensing, data analysis, and statistics, SAR Image Analysis -- A Computational Statistics Approach is also an indispensable resource for researchers, practitioners, and professionals seeking a one-stop resource on how to use statistics to extract information from SAR imagery.

Preface xvii

Acknowledgments xxvii

Acronyms xxxi

Introduction xxxiii

I.1 SAR xxxiii

I.2 Statistics for SAR xxxiv

I.3 The Book xxxv

I.4 Commitment to Reproducibility and Replicability xxxix

1 Data Acquisition 1

1.1 Introduction 1

1.2 SAR 3

1.2.1 The radar 4

1.2.2 What is SAR? 6

1.2.3 SAR systems 10

1.2.4 The synthetic antenna 16

1.3 Spatial resolution 20

1.4 SAR Imaging Techniques 23

1.5 The Return Signal: backscatter and speckle 28

1.5.1 Backscatter 28

1.5.2 Speckle 31

1.5.3 SAR geometric distortions 39

1.6 SAR Satellites 44

1.7 Preprocessing SAR data 53

1.8 Copernicus Open Access Hub 53

1.9 NASA Earth Data Open Data 56

1.10 Actual SAR Data Examples 57

1.10.1 Hawaii's Big Island 57

1.10.2 Other examples 60

Exercises 60

2 Elements of Data Analysis and Image Processing with R 73

2.1 Useful R Packages 73

2.1.1 Data loading 74

2.1.2 Data manipulation 76

2.2 Descriptive Statistics 78

2.2.1 Center tendency of data 78

2.2.2 Dispersion of data 81

2.2.3 Shape of data 84

2.3 Visualization 86

2.3.1 Rug and box plots 87

2.3.2 Histogram 88

2.3.3 Scattering Diagram 92

2.4 Statistics and Image Processing 94

2.4.1 Histogram based Image Transformation 94

2.4.2 Scattering based Analysis 98

2.5 The imagematrix package 101

3 Intensity SAR Data and the Multiplicative Model 105

3.1 The K distribution 115

3.2 The G0 distribution 117

3.3 The GH distribution 121

3.4 Connection between Models 122

Exercises 123

4 Parameter Estimation 127

4.1 Models 128

4.1.1 The Bernoulli distribution 128

4.1.2 The Binomial distribution 128

4.1.3 The Negative Binomial distribution 129

4.1.4 The Uniform distribution 129

4.1.5 Beta distribution 130

4.1.6 The Gaussian distribution 131

4.1.7 Mixture of Gaussian distributions 131

4.1.8 The (SAR) Gamma distribution 132

4.1.9 The Reciprocal Gamma distribution 132

4.1.10 The G0I distribution 133

4.2 Inference by analogy 134

4.2.1 The Uniform distribution 134

4.2.2 The Gaussian distribution 135

4.2.3 Mixture of Gaussian distributions 135

4.2.4 The (SAR) Gamma distribution 136

4.3 Inference by maximum likelihood 136

4.3.1 The Uniform distribution 137

4.3.2 The Gaussian distribution 137

4.3.3 Mixture of Gaussian distributions 138

4.3.4 The (SAR) Gamma distribution 139

4.3.5 The G0 distribution 140

4.4 Analogy vs. Maximum Likelihood 141

4.5 Improvement by bootstrap 142

4.6 Comparison of estimators 143

4.7 An example 144

4.8 The same example, revisited 150

4.9 Another example 152

Exercises 157

5 Applications 159

5.1 Statistical filters: Mean, Median, Lee 160

5.1.1 Mean filter 160

5.1.2 Median filter 164

5.1.3 Lee filter 167

5.2 Advanced filters: MAP and Nonlocal Means 175

5.2.1 MAP Filters 175

5.2.2 Nonlocal Means Filter 177

5.2.3 Statistical NLM filters 183

5.2.4 The statistical test 189

5.3 Implementation Details 191

5.4 Results 193

5.5 Classification 198

5.5.1 The image space of the SAR data 205

5.5.2 The feature space 207

5.5.3 Similarity criterion 210

5.6 Supervised Image Classification of SAR Data 212

5.6.1 The nearest neighbor classifier 214

5.6.2 The K-nn method 219

5.7 Maximum Likelihood Classifier 223

5.8 Unsupervised Image Classification of SAR Data: The K-means classifier 232

5.9 Assessment of Classification Results 236

Exercises 242

6 Advanced Topics 249

6.1 Assessment of Despeckling Filters 249

6.2 Standard Metrics 249

6.2.1 Advanced Metrics for SAR Despeckling Assessment 253

6.2.2 Completing the Assessment 259

6.3 Robustness 259

6.3.1 Robust inference 260

6.3.2 The mean and the median 261

6.3.3 Empirical Stylized Influence Function 266

6.4 Rejoinder and Recommendations 269

7 Reproducibility and Replicability 273

7.1 What Is Reproducibility? 273

7.2 What Is Replicability? 274

7.3 Reproducibility and Replicability: Benefits for the Remote Sensing Community 277

7.4 Recommendations for making "good science" 278

7.5 Conclusions 283

Index 301

Jie Wu, PhD, is Associate Professor at the School of Computer Science, Shaanxi Normal University, China. He received his doctorate in Computer Science and Technology from Xidian University in China.

Luis Gomez, PhD, is Associate Professor at the School of Telecommunications and Electronics Engineering, University of Las Palmas de Gran Canaria, Spain. He received his doctorate in Telecommunication Engineering from the Universidad de Las Palmas de Gran Canaria.