Spatial Analysis for Radar Remote Sensing of Tropical Forests

Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Preface
Acknowledgements
The Authors
List of Abbreviations
List of Figures and Tables
Part I: Sarcheology: The Era of the Big Radar Mosaics
	Chapter 1: The Dawn of the SAR Mosaics Era: The ESA–JRC Central Africa Mosaic Project
		1.1 Radar Mosaics: What and Why
		1.2 The CAMP Data Processing Machine
		1.3 Radiometry
			1.3.1 Radiometric Changes in Time
			1.3.2 Within Tile Radiometric Changes in range
			1.3.3 Quantization Noise
		Note
		References
	Chapter 2: The L-Band Breed: The GRFM Africa Radar Mosaic
		2.1 The GRFM project
		2.2 The GRFM Africa Processing Chain
			2.2.1 Input Datasets
			2.2.2 Data Flow
		2.3 Geolocation
			2.3.1 The Block Adjustment Method
			2.3.2 Geolocation Validation
		2.4 Wavelet Multiresolution Decomposition
			2.4.1 Multiresolution Products
		2.5 The GRFM Africa Mosaic Second Edition
		References
	Chapter 3: The GRFM–CAMP Thematic Products
		3.1 From Backscatter to a Thematic Map
		3.2 Vegetation Classes
		3.3 Map Compilation Methods
		3.4 Complementarity of Radar Sensors
		3.5 Validation
		3.6 Tour of Relevant Features
		References
	Chapter 4: Evolution of the Species: The ALOS PALSAR Africa Mosaic
		4.1 Introduction
		4.2 The Mosaic Processing Chain
		4.3 Correction of Range Dependent Radiometric Bias in Path Images
		4.4 Correction for Additive Thermal Noise in HV Strip Images
		4.5 Radiometric Inter-strip Mosaic Balancing
		4.6 Geocoding
		4.7 Radiometric Normalization for Topographic Effects
			4.7.1 Correction of Effective Scattering Area
			4.7.2 Correction for the Dependence of the Backscattering Coefficient on Incidence Angle
			4.7.3 Assessment of the Radiometric Correction for Topography
		4.8 Overview of the Thematic Information Content
			4.8.1 Comparison with the GRFM Africa Dataset
			4.8.2 Grass and Woody Savannas
			4.8.3 Flooded Forest
			4.8.4 Plantations
			4.8.5 Secondary Forest
		References
Part II: Measures of SAR Random Fields in the Scale–Space–Time Domain
	Chapter 5: The Stuff Backscatter Random Fields Are Made Of
		5.1 Introduction
		5.2 Transport Theory
			5.2.1 An Illustrative Case: Propagation Through A Plane Parallel Medium
		5.3 The UTA Wave Scattering Model for Layered Vegetation
		5.4 Backscatter Simulation for a Dense Tropical Primary Rain Forest
		References
	Chapter 6: Statistical Measures of SAR Random Spatial Fields: Fingerprints of the Forest Structure
		6.1 Introduction
		6.2 Random Fields from Backscatter Observations
		6.3 Random Fields from InSAR Coherence Observations
		6.4 Wavelet Based Textural Measures of Random Fields
		6.5 Connection between Wavelet Space–Scale Analysis and Fourier Spectral Analysis
			6.5.1 White Noise
			6.5.2 1/f Process
			6.5.3 Correlated Surface (Gamma Distributed RCS) with Exponential ACF (Lorentzian Spectrum)
			6.5.4 Correlated Surface with Exponential Cosine ACF
			6.5.5 Effects from Coherent Imaging and Illumination Beam Size
			6.5.6 Cross-correlation between Two Stationary Processes with a Gaussian CCF
		6.6 Accuracy of Wavelet Variance Estimators
			6.6.1 Prelude: Probability Density Function of the Wavelet Coefficients of a Speckle Pattern
			6.6.2 Expected Value and Variance of the Wavelet Variance Estimator
				6.6.2.1 Uncorrelated Speckle Pattern
				6.6.2.2 Correlated Speckle
		6.7 Tools for Textural Analysis of SAR Random Fields
			6.7.1 A Multi-Voice Discrete Wavelet Transform
			6.7.2 Wavelet Signatures
			6.7.3 Wavelet Spectra
		6.8 WASS Analysis of SAR Backscatter Fields
			6.8.1 Lowland Rainforest and Swamp Forest Signatures in ERS-1 Data
			6.8.2 TanDEM-X Signatures in the same Thematic Context
			6.8.3 Intact and Degraded Forest Detection by Functional Analysis of WASS Signatures
		6.9 WASS Analysis of InSAR and LiDAR Digital Surface Models
		6.10 2D Wavelet Variance Spectra of Backscatter Fields: Toward a Textural Classifier
			6.10.1 A Test Case: Texture-Based Forest Mapping in the Congo Floodplain by ERS-1 Data
			6.10.2 Floodplain Mapping Revisited by Sentinel-1 data
			6.10.3 An (Experimental) Wavelet Spectrum Functional Classifier
		6.11 Extension to Polarimetry
			6.11.1 The WASP of Correlated Backscatter Textures: A Numerical Model
			6.11.2 WASP Analysis of a PALSAR Full-Pol Data Set
		Note
		References
	Chapter 7: Hitting Corners: The Lipschitz Regularity, a Measure of Discontinuities in Radar Images Connected with Forest Spatial Distribution
		7.1 Introduction
		7.2 The Lipschitz Condition
		7.3 Singular Functions and Lip Parameters Estimated by Wavelet Maxima Trajectories in the Scale Domain
			7.3.1 Step Function
			7.3.2 Cusp
			7.3.3 Impulse
			7.3.4 Smoothed Singularity
			7.3.5 Non-Isolated Singularities
			7.3.6 Effect of Speckle
		7.4 A Monte Carlo Simulator of Polarimetric SAR Backscatter Discontinuities
		7.5 Experiments Using Simulated Signals
			7.5.1 Toy Signals with Simple Discontinuities
			7.5.2 Margin between a Clear-Cut and a Dense Forest
			7.5.3 Edge on Tilted Terrain
		7.6 Lipschitz Regularity in Real SAR Data
			7.6.1 TanDEM-X Backscatter Data
			7.6.2 TanDEM-X Coherence Data
		7.7 Image-Wide Representations of Lipschitz Parameters
		References
	Chapter 8: The Beauty Farm: A Wavelet Method for Edge Preserving Piece-wise Smooth Approximations of Radar Images
		8.1 The Image Model and a Conceptual View of the Method
		8.2 The Computational Engine
		8.3 Problems Related to Multiplicative Speckle Noise
		8.4 Issues Related to Textural Edges
		8.5 Maxima Linking
		8.6 From Theory to Practice: A Tropical Forest Cover Mapping Exercise Using Smooth Approximations of GRFM SAR Data
			8.6.1 Processing Methods
				8.6.1.1 Region Growing
				8.6.1.2 NMP Classifier
			8.6.2 Test Sites and Thematic Class Definition
			8.6.3 Selected Results
		References
	Chapter 9: The Cleaning Service: A Multi-temporal InSAR Coherence Magnitude Filter
		9.1 Rationale
		9.2 The Filter Machinery
		9.3 Generation of a Testing Dataset
		9.4 Test Cases Using TanDEM-X Data
		9.5 Temporal Features
		References
	Chapter 10: Proxies of Forest Volume Loss and Gain by Differencing InSAR DSMs: Fingerprints of Forest Disturbance
		10.1 Motivation
		10.2 Study Site
		10.3 TanDEM-X Data
		10.4 Methods
			10.4.1 DSM Difference Data Set Generation and Calibration
			10.4.2 Object-Based Change Detection
			10.4.3 Change Objects Refinement
			10.4.4 Variance of the Within-Object Mean Height Difference Estimator
			10.4.5 Effect Size
				10.4.6 Probability of object detection by statistical decision theory
				10.4.6.1 Neyman–Pearson approach
				10.4.6.2 Bayesian Approach
			10.4.7 Object Shape
			10.4.8 Characterization of Objects by Contextual Information
				10.4.8.1 Distance from Roads
				10.4.8.2 Attributes by Land Management
		10.5 Factors Influencing the DSM Change Magnitude
			10.5.1 Forest Vertical Structure and Spatial Distribution (Forest Density)
			10.5.2 Environmental Conditions (Seasonality and Rainfall)
			10.5.3 Dependence on Instrument Parameters
				10.5.3.1 Volume Only
				10.5.3.2 Volume over Ground
		10.6 Analysis
			10.6.1 ∆ DSM Magnitude and Area Descriptive Statistic
			10.6.2 Standard Error of the Object Mean
			10.6.3 Effect Size
			10.6.4 Object Detection by Statistical Decision Theory
			10.6.5 Spatial Location of Objects
			10.6.6 Objects’ Proximity to Roads
			10.6.7 Change in Objects by Land Management
			10.6.8 Shape Analysis
				10.6.8.1 Fractal Exponent
				10.6.8.2 Rectangularity
				10.6.8.3 Regular Boundary Shapes in Land Management Units
		10.7 Comparison between Objects Detected by InSAR ΔDSM and by Optical Imagery
		10.8 Concluding Remarks
		References
Appendix: A Wavelet Tour
	A.1 Signal Representation in a Basis
	A.2 The Fourier Kingdom
	A.3 Extension to Linear Transforms with More Interesting Atoms – Where Wavelets Finally Appear
	A.4 The Wavelet Transform in a Discrete Time Setting
	A.5 Computing the Wavelet Frame Transform: The “à trous” Algorithm
	A.6 The Multiresolution Wavelet Representation
	References
Index
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