Image Processing for Remote Sensing - Chapter 1 ppsx

3 1.2.3 Measurement of Ocean Wave Slopes Using Polarimetric SAR Data .... Algorithms, pre-sented here, to measure directional wave spectra, wave slopes, wave–current interactions,and cur

Image Processing

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Remote

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Image Processing for
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Edited
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Library of Congress Cataloging-in-Publication Data

Image processing for remote sensing / [edited by] C.H Chen.

This volume is a spin-off edition derived from Signal and Image Processing for RemoteSensing It presents more advanced topics of image processing in remote sensing thansimilar books in the area The topics of image modeling, statistical image classifiers,change detection, independent component analysis, vertex component analysis, imagefusion for better classification or segmentation, 2-D time series modeling, neural networkclassifications, etc are examined in this volume Some unique topics like accuracy assess-ment and information-theoretic measure of multiband images are presented An em-phasis is placed on the issues with synthetic aperture radar (SAR) images in manychapters Continued development on imaging sensors always presents new opportunitiesand challenges on image processing for remote sensing The hyperspectral imagingsensor is a good example here We believe this volume not only presents the most up-to-date developments of image processing for remote sensing but also suggests to readersthe many challenging problems ahead for further study

Original Preface fromSignal and Image Processing for Remote Sensing

Both signal processing and image processing have been playing increasingly importantroles in remote sensing While most data from satellites are in image forms and thusimage processing has been used most often, signal processing can contribute significantly

in extracting information from the remotely sensed waveforms or time series data Incontrast to other books in this field which deal almost exclusively with the imageprocessing for remote sensing, this book provides a good balance between the roles ofsignal processing and image processing in remote sensing The book covers mainlymethodologies of signal processing and image processing in remote sensing Emphasis

is thus placed on the mathematical techniques which we believe will be less changed ascompared to sensor, software and hardware technologies Furthermore, the term ‘‘remotesensing’’ is not limited to the problems with data from satellite sensors Other sensorswhich acquire data remotely are also considered Thus another unique feature of the book

is the coverage of a broader scope of the remote sensing information processing problemsthan any other book in the area

The book is divided into two parts [now published as separate volumes under thefollowing titles] Part I, Signal Processing for Remote Sensing, has 12 chapters and Part II[comprising the present volume], Image Processing for Remote Sensing, has 16 chapters Thechapters are written by leaders in the field We are very fortunate, for example, to have

Dr Norden Huang, inventor of the Huang–Hilbert transform, along with Dr StevenLong, to write a chapter on the application of the transform to remote sensing problem,and Dr Enders A Robinson, who has made many major contributions to geophysicalsignal processing for over half a century, to write a chapter on the basic problem ofconstructing seismic images by ray tracing

In Part I, following Chapter 1 by Drs Long and Huang, and my short Chapter 2 on theroles of statistical pattern recognition and statistical signal processing in remote sensing,

we start from a very low end of the electromagnetic spectrum Chapter 3 considers theclassification of infrasound at a frequency range of 0.001 Hz to 10 Hz by using a parallelbank neural network classifier and a 11-step feature selection process The >90% correctclassification rate is impressive for this kind of remote sensing data Chapter 4 through

Chapter 6 deal with seismic signal processing Chapter 4 provides excellent physicalinsights on the steps for construction of digital seismic images Even though the seismicimage is an image, this chapter is placed in Part I as seismic signals start as waveforms.Chapter 5 considers the singular value decomposition of a matrix data set from scalar-sensors arrays, which is followed by independent component analysis (ICA) step to relaxthe unjustified orthogonality constraint for the propagation vectors by imposing astronger constraint of fourth-order independence of the estimated waves With an initialfocus of the use of ICA in seismic data and inspired by Dr Robinson’s lecture on seismicdeconvolution at the 4th International Symposium, 2002, on Computer Aided SeismicAnalysis and Discrimination, Mr Zhenhai Wang has examined approaches beyond ICAfor improving seismic images Chapter 6 is an effort to show that factor analysis, as analternative to stacking, can play a useful role in removing some unwanted components inthe data and thereby enhancing the subsurface structure as shown in the seismic images.Chapter 7 on Kalman filtering for improving detection of landmines using electromag-netic signals, which experience severe interference, is another remote sensing problem ofhigher interest in recent years Chapter 8 is a representative time series analysis problem

on using meteorological and remote sensing indices to monitor vegetation moisturedynamics Chapter 9 actually deals with the image data for digital elevation model but

is placed in Part I mainly because the prediction error (PE) filter is originated from thegeophysical signal processing The PE filter allows us to interpolate the missing parts of

an image The only chapter that deals with the sonar data is Chapter 10, which shows that

a simple blind source separation algorithm based on the second-order statistics can bevery effective to remove reverberations in active sonar data Chapter 11 and Chapter 12are excellent examples of using neural networks for retrieval of physical parameters fromthe remote sensing data Chapter 12 further provides a link between signal and imageprocessing as the principal component analysis and image sharpening tools employed areexactly what are needed in Part II

With a focus on image processing of remote sensing images, Part II begins with Chapter

13 [Chapter 1of the present volume] that is concerned with the physics and mathematicalalgorithms for determining the ocean surface parameters from synthetic aperture radar(SAR) images Mathematically Markov random field (MRF) is one of the most usefulmodels for the rich contextual information in an image Chapter 14 [now Chapter 2]provides a comprehensive treatment of MRF-based remote sensing image classification.Besides an overview of previous work, the chapter describes the methodological issuesinvolved and presents results of the application of the technique to the classification ofreal (both single-date and multitemporal) remote sensing images Although there aremany studies on using an ensemble of classifiers to improve the overall classificationperformance, the random forest machine learning method for classification of hyperspec-tral and multisource data as presented in Chapter 15 [now Chapter 3] is an excellentexample of using new statistical approaches for improved classification with the remotesensing data Chapter 16 [now Chapter 4] presents another machine learning method,AdaBoost, to obtain robustness property in the classifier The chapter further considersthe relations among the contextual classifier, MRF-based methods, and spatial boosting.The following two chapters are concerned with different aspects of the change detectionproblem Change detection is a uniquely important problem in remote sensing as theimages acquired at different times over the same geographical area can be used in theareas of environmental monitoring, damage management, and so on After discussingchange detection methods for multitemporal SAR images, Chapter 17 [now Chapter 5]examines an adaptive scale–driven technique for change detection in medium resolu-tion SAR data Chapter 18 [now Chapter 6] evaluates the Wiener filter-based method,

Mahalanobis distance, and subspace projection methods of change detection, with thechange detection performance illustrated by receiver operating characteristics (ROC)curves In recent years, ICA and related approaches have presented many new potentials

in remote sensing information processing A challenging task underlying many spectral imagery applications is decomposing a mixed pixel into a collection of reflec-tance spectra, called endmember signatures, and the corresponding abundance fractions.Chapter 19 [now Chapter 7] presents a new method for unsupervised endmemberextraction called vertex component analysis (VCA) The VCA algorithms presentedhave better or comparable performance as compared to two other techniques but requireless computational complexity Other useful ICA applications in remote sensing includefeature extraction, and speckle reduction of SAR images Chapter 20 [now Chapter 8]presents two different methods of SAR image speckle reduction using ICA, both makinguse of the FastICA algorithm In two-dimensional time series modeling, Chapter 21 [now

hyper-Chapter 9] makes use of a fractionally integrated autoregressive moving average(FARIMA) analysis to model the mean radial power spectral density of the sea SARimagery Long-range dependence models are used in addition to the fractional sea surfacemodels for the simulation of the sea SAR image spectra at different sea states, with andwithout oil slicks at low computational cost

Returning to the image classification problem, Chapter 22 [nowChapter 10] deals withthe topics of pixel classification using Bayes classifier, region segmentation guided bymorphology and split-and-merge algorithm, region feature extraction, and region classi-fication

Chapter 23 [nowChapter 11] provides a tutorial presentation of different issues of datafusion for remote sensing applications Data fusion can improve classification and for thedecision level fusion strategies, four multisensor classifiers are presented Beyond thecurrently popular transform techniques, Chapter 24 [nowChapter 12] demonstrates thatHermite transform can be very useful for noise reduction and image fusion in remotesensing The Hermite transform is an image representation model that mimics some of theimportant properties of human visual perception, namely local orientation analysis andthe Gaussian derivative model of early vision Chapter 25 [now Chapter 13] is anotherchapter that demonstrates the importance of image fusion to improving sea ice classifi-cation performance, using backpropagation trained neural network and linear discrimin-ation analysis and texture features Chapter 26 [now Chapter 14] is on the issue ofaccuracy assessment for which the Bradley–Terry model is adopted Chapter 27 [now

Chapter 15] is on land map classification using support vector machine, which has beenincreasingly popular as an effective classifier The land map classification classifies thesurface of the Earth into categories such as water area, forests, factories or cities Finally,with lossless data compression in mind, Chapter 28 [nowChapter 16] focuses on infor-mation-theoretic measure of the quality of multi-band remotely sensed digital images.The procedure relies on the estimation of parameters of the noise model Results on imagesequences acquired by AVIRIS and ASTER imaging sensors offer an estimation of theinformation contents of each spectral band

With rapid technological advances in both sensor and processing technologies, a book

of this nature can only capture certain amount of current progress and results However,

if past experience offers any indication, the numerous mathematical techniques presentedwill give this volume a long lasting value

The sister volumes of this book are the other two books edited by myself One isInformation Processing for Remote Sensing and the other is Frontiers of Remote SensingInformation Processing, both published by World Scientific in 1999 and 2003, respectively

I am grateful to all contributors of this volume for their important contribution and,

in particular, to Dr J.S Lee, S Serpico, L Bruzzone and S Omatu for chapter tions to all three volumes Readers are advised to go over all three volumes for a morecomplete information on signal and image processing for remote sensing.

contribu-C H Chen

Chi Hau Chen was born on December 22nd, 1937 He received his Ph.D in electricalengineering from Purdue University in 1965, M.S.E.E degree from the University ofTennessee, Knoxville, in 1962, and B.S.E.E degree from the National Taiwan University

in 1959

He is currently chancellor professor of electrical and computer engineering at theUniversity of Massachusetts, Dartmouth, where he has taught since 1968 His researchareas are in statistical pattern recognition and signal/image processing with applications

to remote sensing, geophysical, underwater acoustics, and nondestructive testing lems, as well as computer vision for video surveillance, time series analysis, and neuralnetworks

prob-Dr Chen has published 25 books in his area of research He is the editor of DigitalWaveform Processing and Recognition (CRC Press, 1982) and Signal Processing Handbook(Marcel Dekker, 1988) He is the chief editor of Handbook of Pattern Recognition andComputer Vision, volumes 1, 2, and 3 (World Scientific Publishing, 1993, 1999, and 2005,respectively) He is the editor of Fuzzy Logic and Neural Network Handbook (McGraw-Hill,1966) In the area of remote sensing, he is the editor of Information Processing for RemoteSensing and Frontiers of Remote Sensing Information Processing (World Scientific Publishing,

1999 and 2003, respectively)

He served as the associate editor of the IEEE Transactions on Acoustics Speech and SignalProcessing for 4 years, IEEE Transactions on Geoscience and Remote Sensing for 15 years, andsince 1986 he has been the associate editor of the International Journal of Pattern Recognitionand Artificial Intelligence

Dr Chen has been a fellow of the Institutue of Electrical and Electronic Engineers(IEEE) since 1988, a life fellow of the IEEE since 2003, and a fellow of the InternationalAssociation of Pattern Recognition (IAPR) since 1996

Bruno Aiazzi Institute of Applied Physics, National Research Council, Florence, Italy

Center, St Petersburg, Russia

Luciano Alparone Department of Electronics and Telecommunications, University

of Florence, Florence, Italy

Stefano Baronti Institute of Applied Physics, National Research Council, Florence,Italy

University of Iceland, Reykjavik, Iceland

Fabrizio Berizzi Department of Information Engineering, University of Pisa, Pisa, Italy

Analysis and Signal Processing, Pisa, Italy

St Petersburg, Russia

University of Trento, Trento, Italy

University of Trento, Trento, Italy

Chi Hau Chen Department of Electrical and Computer Engineering, University ofMassachusetts Dartmouth, North Dartmouth, Massachusetts

Salim Chitroub Signal and Image Processing Laboratory, Department of munication, Algiers, Algeria

Superior Te´cnico, Av Rovisco Pais, Lisbon, Portugal

Shinto Eguchi Institute of Statistical Mathematics, Tokyo, Japan

Boris Escalante-Ramı´rez School of Engineering, National Autonomous University

of Mexico, Mexico City, Mexico

Toru Fujinaka Osaka Prefecture University, Osaka, Japan

Gerrit Gort Department of Biometris, Wageningen University, The NetherlandsSveinn R Joelsson Department of Electrical and Computer Engineering, University

of Iceland, Reykjavik, Iceland

Norway

Dayalan Kasilingam Department of Electrical and Computer Engineering, sity of Massachusetts Dartmouth, North Dartmouth, Massachusetts

Jong-Sen Lee Remote Sensing Division, Naval Research Laboratory, Washington, D.C.Alejandra A Lo´pez-Caloca Center for Geography and Geomatics Research, MexicoCity, Mexico

Arko Lucieer Centre for Spatial Information Science (CenSIS), University of mania, Australia

Tas-Enzo Dalle Mese Department of Information Engineering, University of Pisa, Pisa,Italy

Gabriele Moser Department of Biophysical and Electronic Engineering, University

of Genoa, Genoa, Italy

Jose´ M.P Nascimento Instituto Superior, de Eugenharia de Lisbon, Lisbon, Portugal

Ryuei Nishii Faculty of Mathematics, Kyusyu University, Fukuoka, Japan

Sigeru Omatu Osaka Prefecture University, Osaka, Japan

Dale L Schuler Remote Sensing Division, Naval Research Laboratory, Washington,D.C

Massimo Selva Institute of Applied Physics, National Research Council, Florence,Italy

Sebastiano B Serpico Department of Biophysical and Electronic Engineering,University of Genoa, Genoa, Italy

Anne H.S Solberg Department of Informatics, University of Oslo and NorwegianComputing Center, Oslo, Norway

Alfred Stein International Institute for Geo-Information Science and Earth vation, Enschede, The Netherlands

University of Iceland, Reykjavik, Iceland

Maria Tates U.S Army Research Laboratory, Adelphi, Maryland, and Morgan StateUniversity, Baltimore, Maryland

Massachusetts Dartmouth, North Dartmouth, Massachusetts

Carl White Morgan State University, Baltimore, Maryland

Michifumi Yoshioka Osaka Prefecture University, Osaka, Japan

1 Polarimetric SAR Techniques for Remote Sensing of the Ocean Surface 1

Dale L Schuler, Jong-Sen Lee, and Dayalan Kasilingam

2 MRF-Based Remote-Sensing Image Classification with

Automatic Model Parameter Estimation 39

Sebastiano B Serpico and Gabriele Moser

3 Random Forest Classification of Remote Sensing Data 61

Sveinn R Joelsson, Jon Atli Benediktsson, and Johannes R Sveinsson

4 Supervised Image Classification of Multi-Spectral Images

Based on Statistical Machine Learning 79

Ryuei Nishii and Shinto Eguchi

5 Unsupervised Change Detection in Multi-Temporal SAR Images 107

Lorenzo Bruzzone and Francesca Bovolo

6 Change-Detection Methods for Location of Mines in SAR Imagery 135

Maria Tates, Nasser Nasrabadi, Heesung Kwon, and Carl White

7 Vertex Component Analysis: A Geometric-Based

Approach to Unmix Hyperspectral Data 149

Jose´ M.B Dias and Jose´ M.P Nascimento

8 Two ICA Approaches for SAR Image Enhancement 175

Chi Hau Chen, Xianju Wang, and Salim Chitroub

9 Long-Range Dependence Models for the Analysis and

Discrimination of Sea-Surface Anomalies in Sea SAR Imagery 189

Massimo Bertacca, Fabrizio Berizzi, and Enzo Dalle Mese

10 Spatial Techniques for Image Classification 225

Selim Aksoy

11 Data Fusion for Remote-Sensing Applications 249

Anne H.S Solberg

12 The Hermite Transform: An Efficient Tool for Noise Reduction

and Image Fusion in Remote-Sensing 273

Boris Escalante-Ramı´rez and Alejandra A Lo´pez-Caloca

13 Multi-Sensor Approach to Automated Classification of Sea Ice Image Data 293

A.V Bogdanov, S Sandven, O.M Johannessen, V.Yu Alexandrov, and L.P Bobylev

14 Use of the Bradley–Terry Model to Assess Uncertainty in an

Error Matrix from a Hierarchical Segmentation of an ASTER Image 325

Alfred Stein, Gerrit Gort, and Arko Lucieer

15 SAR Image Classification by Support Vector Machine 341

Michifumi Yoshioka, Toru Fujinaka, and Sigeru Omatu

16 Quality Assessment of Remote-Sensing Multi-Band Optical Images 355

Bruno Aiazzi, Luciano Alparone, Stefano Baronti, and Massimo Selva

Polarimetric SAR Techniques for Remote

Sensing of the Ocean Surface

Dale L Schuler, Jong-Sen Lee, and Dayalan Kasilingam

CONTENTS

1.1 Introduction 2

1.2 Measurement of Directional Slopes and Wave Spectra 2

1.2.1 Single Polarization versus Fully Polarimetric SAR Techniques 2

1.2.2 Single-Polarization SAR Measurements of Ocean Surface Properties 3

1.2.3 Measurement of Ocean Wave Slopes Using Polarimetric SAR Data 5

1.2.3.1 Orientation Angle Measurement of Azimuth Slopes 5

1.2.3.2 Orientation Angle Measurement Using the Circular-Pol Algorithm 5

1.2.4 Ocean Wave Spectra Measured Using Orientation Angles 6

1.2.5 Two-Scale Ocean-Scattering Model: Effect on the Orientation Angle Measurement 9

1.2.6 Alpha Parameter Measurement of Range Slopes 11

1.2.6.1 Cloude–Pottier Decomposition Theorem and the Alpha Parameter 11

1.2.6.2 Alpha Parameter Sensitivity to Range Traveling Waves 13

1.2.6.3 Alpha Parameter Measurement of Range Slopes and Wave Spectra 14

1.2.7 Measured Wave Properties and Comparisons with Buoy Data 16

1.2.7.1 Coastal Wave Measurements: Gualala River Study Site 16

1.2.7.2 Open-Ocean Measurements: San Francisco Study Site 18

1.3 Polarimetric Measurement of Ocean Wave–Current Interactions 20

1.3.1 Introduction 20

1.3.2 Orientation Angle Changes Caused by Wave–Current Interactions 21

1.3.3 Orientation Angle Changes at Ocean Current Fronts 25

1.3.4 Modeling SAR Images of Wave–Current Interactions 25

1.4 Ocean Surface Feature Mapping Using Current-Driven Slick Patterns 27

1.4.1 Introduction 27

1.4.2 Classification Algorithm 31

1.4.2.1 Unsupervised Classification of Ocean Surface Features 31

1.4.2.2 Classification Using Alpha–Entropy Values and the Wishart Classifier 31

1.4.2.3 Comparative Mapping of Slicks Using Other Classification Algorithms 34

1.5 Conclusions 34

References 36

1

1.1 Introduction

Selected methods that use synthetic aperture radar (SAR) image data to remotely senseocean surfaces are described in this chapter Fully polarimetric SAR radars provide muchmore usable information than conventional single-polarization radars Algorithms, pre-sented here, to measure directional wave spectra, wave slopes, wave–current interactions,and current-driven surface features use this additional information

Polarimetric techniques that measure directional wave slopes and spectra with datacollected from a single aircraft, or satellite, collection pass are described here Conven-tional single-polarization backscatter cross-section measurements require two orthogonalpasses and a complex SAR modulation transfer function (MTF) to determine vector slopesand directional wave spectra

The algorithm to measure wave spectra is described in Section 1.2 In the azimuth(flight) direction, wave-induced perturbations of the polarimetric orientation angle areused to sense the azimuth component of the wave slopes In the orthogonal rangedirection, a technique involving an alpha parameter from the well-known Cloude–Pottierentropy/anisotropy/averaged alpha (H/A/ 
) polarimetric decomposition theorem isused to measure the range slope component Both measurement types are highly sensitive

to ocean wave slopes and are directional Together, they form a means of using metric SAR image data to make complete directional measurements of ocean wave slopesand wave slope spectra

polari-NASA Jet Propulsion Laboratory airborne SAR (AIRSAR) P-, L-, and C-band dataobtained during flights over the coastal areas of California are used as wave-fieldexamples Wave parameters measured using the polarimetric methods are compared withthose obtained using in situ NOAA National Data Buoy Center (NDBC) buoy products

In a second topic (Section 1.3), polarization orientation angles are used to remotelysense ocean wave slope distribution changes caused by ocean wave–current interactions.The wave–current features studied include surface manifestations of ocean internalwaves and wave interactions with current fronts

A model [1], developed at the Naval Research Laboratory (NRL), is used to determinethe parametric dependencies of the orientation angle on internal wave current, wind-wave direction, and wind-wave speed An empirical relation is cited to relate orientationangle perturbations to the underlying parametric dependencies [1]

A third topic (Section 1.4) deals with the detection and classification of biogenic slickfields Various techniques, using the Cloude–Pottier decomposition and Wishart clas-sifier, are used to classify the slicks An application utilizing current-driven oceanfeatures, marked by slick patterns, is used to map spiral eddies Finally, a relatedtechnique, using the polarimetric orientation angle, is used to segment slick fields fromocean wave slopes

1.2 Measurement of Directional Slopes and Wave Spectra

1.2.1 Single Polarization versus Fully Polarimetric SAR Techniques

SAR systems conventionally use backscatter intensity-based algorithms [2] to measurephysical ocean wave parameters SAR instruments, operating at a single-polarization,measure wave-induced backscatter cross section, or sigma-0, modulations that can be

developed into estimates of surface wave slopes or wave spectra These measurements,however, require a parametrically complex MTF to relate the SAR backscatter meas-urements to the physical ocean wave properties [3].

Section 1.2.3 through Section 1.2.6 outline a means of using fully polarimetric SAR(POLSAR) data with algorithms [4] to measure ocean wave slopes In the Fourier-trans-form domain, this orthogonal slope information is used to estimate a complete directionalocean wave slope spectrum A parametrically simple measurement of the slope is made

by using POLSAR-based algorithms

Modulations of the polarization orientation angle, u, are largely caused by wavestraveling in the azimuth direction The modulations are, to a lesser extent, also affected

by range traveling waves A method, originally used in topographic measurements [5],has been applied to the ocean and used to measure wave slopes The method measuresvector components of ocean wave slopes and wave spectra Slopes smaller than 18 aremeasurable for ocean surfaces using this method

An eigenvector or eigenvalue decomposition average parameter 
, described in Ref.[6], is used to measure wave slopes in the orthogonal range direction Waves in therange direction cause modulation of the local incidence angle f, which, in turn, changesthe value of 
The alpha parameter is ‘‘roll-invariant.’’ This means that it is not affected

by slopes in the azimuth direction Likewise, for ocean wave measurements, the tation angle u parameter is largely insensitive to slopes in the range direction Analgorithm employing both ( 
, u) is, therefore, capable of measuring slopes in anydirection The ability to measure a physical parameter in two orthogonal directionswithin an individual resolution cell is rare Microwave instruments, generally, musthave a two-dimensional (2D) imaging or scanning capability to obtain information intwo orthogonal directions

orien-Motion-induced nonlinear ‘‘velocity-bunching’’ effects still present difficulties for wavemeasurements in the azimuth direction using POLSAR data These difficulties are dealtwith by using the same proven algorithms [3,7] that reduce nonlinearities for single-polarization SAR measurements

1.2.2 Single-Polarization SAR Measurements of Ocean Surface Properties

SAR systems have previously been used for imaging ocean features such as surfacewaves, shallow-water bathymetry, internal waves, current boundaries, slicks, and shipwakes [8] In all of these applications, the modulation of the SAR image intensity by theocean feature makes the feature visible in the image [9] When imaging ocean surfacewaves, the main modulation mechanisms have been identified as tilt modulation, hydro-dynamic modulation, and velocity bunching [2] Tilt modulation is due to changes in thelocal incidence angle caused by the surface wave slopes [10] Tilt modulation is strongestfor waves traveling in the range direction Hydrodynamic modulation is due to thehydrodynamic interactions between the long-scale surface waves and the short-scalesurface (Bragg) waves that contribute most of the backscatter at moderate incidenceangles [11] Velocity bunching is a modulation process that is unique to SAR imagingsystems [12] It is a result of the azimuth shifting of scatterers in the image plane, owing

to the motion of the scattering surface Velocity bunching is the highest for azimuthtraveling waves

In the past, considerable effort had gone into retrieving quantitative surface waveinformation from SAR images of ocean surface waves [13] Data from satellite SARmissions, such as ERS 1 and 2 and RADARSAT 1 and 2, had been used to estimatesurface wave spectra from SAR image information Generally, wave height and wavePolarimetric SAR Techniques for Remote Sensing of the Ocean Surface 3

slope spectra are used as quantitative overall descriptors of the ocean surface waveproperties [14] Over the years, several different techniques have been developed forretrieving wave spectra from SAR image spectra [7,15,16] Linear techniques, such asthose having a linear MTF, are used to relate the wave spectrum to the imagespectrum Individual MTFs are derived for the three primary modulation mechanisms.

A transformation based on the MTF is used to retrieve the wave spectrum from theSAR image spectrum Since the technique is linear, it does not account for any non-linear processes in the modulation mechanisms It has been shown that SAR imagemodulation is nonlinear under certain ocean surface conditions As the sea stateincreases, the degree of nonlinear behavior generally increases Under these conditions,the linear methods do not provide accurate quantitative estimates of the wave spectra[15] Thus, the linear transfer function method has limited utility and can be used as aqualitative indicator More accurate estimates of wave spectra require the use of non-linear inversion techniques [15]

Several nonlinear inversion techniques have been developed for retrieving wavespectra from SAR image spectra Most of these techniques are based on a techniquedeveloped in Ref [7] The original method used an iterative technique to estimate thewave spectrum from the image spectrum Initial estimates are obtained using a lineartransfer function similar to the one used in Ref [15] These estimates are used as inputs

in the forward SAR imaging model, and the revised image spectrum is used toiteratively correct the previous estimate of the wave spectra The accuracy of thistechnique is dependent on the specific SAR imaging model Improvements to thistechnique [17] have incorporated closed-form descriptions of the nonlinear transferfunction, which relates the wave spectrum to the SAR image spectrum However,this transfer function also has to be evaluated iteratively Further improvements tothis method have been suggested in Refs [3,18] In this method, a cross-spectrum isgenerated between different looks of the same ocean wave scene The primary advan-tage of this method is that it resolves the 1808 ambiguity [3,18] of the wave direction.This method also reduces the effects of speckle in the SAR spectrum Methods thatincorporate additional a posteriori information about the wave field, which improvesthe accuracy of these nonlinear methods, have also been developed in recent years [19]

In all of the slope-retrieval methods, the one nonlinear mechanism that may completelydestroy wave structure is velocity bunching [3,7] Velocity bunching is a result of movingscatterers on the ocean surface either bunching or dilating in the SAR image domain Theshifting of the scatterers in the azimuth direction may, in extreme conditions, result in thedestruction of the wave structure in the SAR image

SAR imaging simulations were performed at different range-to-velocity (R/V) ratios tostudy the effect of velocity bunching on the slope-retrieval algorithms When the (R/V)ratio is artificially increased to large values, the effects of velocity bunching are expected

to destroy the wave structure in the slope estimates Simulations of the imaging processfor a wide range of radar-viewing conditions indicate that the slope structure is preserved

in the presence of moderate velocity-bunching modulation It can be argued that forvelocity bunching to affect the slope estimates, the (R/V) ratio has to be significantlylarger than 100 s The two data sets discussed here are designated ‘‘Gualala River’’ and

‘‘San Francisco.’’ The Gualala river data set has the longest waves and it also produces thebest results The R/V ratio for the AIRSAR missions was 59 s (Gualala) and 55 s (SanFrancisco) These values suggest that the effects of velocity bunching are present, but arenot sufficiently strong to significantly affect the slope-retrieval process However, forspaceborne SAR imaging applications, where the (R / V) ratio may be greater than 100 s,the effects of velocity bunching may limit the utility of all methods, especially in highsea states

1.2.3 Measurement of Ocean Wave Slopes Using Polarimetric SAR Data

In this section, the techniques that were developed for the measurement of ocean surfaceslopes and wave spectra using the capabilities of fully polarimetric radars are discussed.Wave-induced perturbations of the polarization orientation angle are used to directlymeasure slopes for azimuth traveling waves This technique is accurate for scatteringfrom surface resolution cells where the sea return can be represented as a two-scaleBragg-scattering process

1.2.3.1 Orientation Angle Measurement of Azimuth Slopes

It has been shown [5] that by measuring the orientation angle shift in the polarizationsignature, one can determine the effects of the azimuth surface tilts In particular, the shift inthe orientation angle is related to the azimuth surface tilt, the local incidence angle, and, to alesser degree, the range tilt This relationship is derived [20] and independently verified [6] as

tan u ¼ tan v

sin f
tan g cos f (1:1)where u, tan v, tan g, and f are the shifts in the orientation angle, the azimuth slope, theground range slope, and the radar look angle, respectively According to Equation 1.1, theazimuth tilts may be estimated from the shift in the orientation angle, if the look angle andrange tilt are known

The orthogonal range slope tan g can be estimated using the value of the local incidenceangle associated with the alpha parameter for each pixel The azimuth slope tan v and therange slope tan g provide complete slope information for each image pixel

For the ocean surface at scales of the size of the AIRSAR resolution cell (6.6 m  8.2 m),the averaged tilt angles are small and the denominator in Equation 1.1 may be approxi-mated by sin f for a wide range of look angles, cos f, and ground range slope, tan g,values Under this approximation, the ocean azimuth slope, tan v, is written as

tan v ffi ( sin f)  tan u (1:2)The above equation is important because it provides a direct link between polarimetric SARmeasurable parameters and physical slopes on the ocean surface This estimation of ocean slopesrelies only on (1) the knowledge of the radar look angle (generally known from the SAR viewinggeometry) and (2) the measurement of the wave-perturbed orientation angle In ocean areaswhere the average scattering mechanism is predominantly tilted-Bragg scatter, the orientationangle can be measured accurately for angular changes <18, as demonstrated in Ref [20].POLSAR data can be represented by the scattering matrix for single-look complex dataand by the Stokes matrix, the covariance matrix, or the coherency matrix for multi-lookdata An orientation angle shift causes rotation of all these matrices about the line of sight.Several methods have been developed to estimate the azimuth slope–induced orientationangles for terrain and ocean applications The ‘‘polarization signature maximum’’ methodand the ‘‘circular polarization’’ method have proven to be the two most effective methods.Complete details of these methods and the relation of the orientation angle to orthogonalslopes and radar parameters are given [21,22]

1.2.3.2 Orientation Angle Measurement Using the Circular-Pol Algorithm

Image processing was done with both the polarization signature maximum and thecircular polarization algorithms The results indicate that for ocean images a sign-ificant improvement in wave visibility is achieved when a circular polarization algor-ithm is chosen In addition to this improvement, the circular polarization algorithm isPolarimetric SAR Techniques for Remote Sensing of the Ocean Surface 5

computationally more efficient Therefore, the circular polarization algorithm methodwas chosen to estimate orientation angles The most sensitive circular polarization esti-mator [21], which involves RR (right-hand transmit, right-hand receive) and LL (left-handtransmit, left-hand receive) terms, is

u¼ [Arg(hSRRS*LLi) þ p]=4 (1:3)

A linear-pol basis has a similar transmit-and-receive convention, but the terms (HH, VV,

HV, VH) involve horizontal (H) and vertical (V) transmitted, or received, components.The known relations between a circular-pol basis and a linear-pol basis are

SRR¼ (SHH
SVVþ i2SHV)=2

SLL¼ (SVV
SHHþ i2SHV)=2 (1:4)Using the above equation, the Arg term of Equation 1.3 can be written as

1.2.4 Ocean Wave Spectra Measured Using Orientation Angles

NASA/JPL/AIRSAR data were taken (1994) at L-band imaging a northern Californiacoastal area near the town of Gualala (Mendocino County) and the Gualala River Thisdata set was used to determine if the azimuth component of an ocean wave spectrumcould be measured using orientation angle modulation The radar resolution cell haddimensions of 6.6 m (range direction) and 8.2 m (azimuth direction), and 3  3 boxcaraveraging was done to the data inputted into the orientation angle algorithms

Figure 1.1 is an L-band, VV-pol, pseudo color-coded image of a northern Californiacoastal area and the selected measurement study site A wave system with an estimateddominant wavelength of 157 m is propagating through the site with a wind-wavedirection of 3068 (estimates from wave spectra,Figure 1.4) The scattering geometry for

a single average tilt radar resolution cell is shown in Figure 1.2 Modulations in thepolarization orientation angle induced by azimuth traveling ocean waves in the studyarea are shown inFigure 1.3aand a histogram of the orientation angles is given inFigure1.3b An orientation angle spectrum versus wave number for azimuth direction wavespropagating in the study area is given in Figure 1.4 The white rings correspond to oceanwavelengths of 50, 100, 150, and 200 m The dominant 157-m wave is propagating at aheading of 3068.Figure 1.5aand Figure 1.5b give plots of spectral intensity versus wavenumber (a) for wave-induced orientation angle modulations and (b) for single-polariza-tion (VV-pol)-intensity modulations The plots are of wave spectra taken in the directionthat maximizes the dominant wave peak The orientation angle–dominant wave peak

(Figure 1.5a) has a significantly higher signal and background ratio than the conventionalintensity-based VV-pol-dominant wave peak (Figure 1.5b).

Finally, the orientation angles measured within the study sites were converted intoazimuth direction slopes using an average incidence angle and Equation 1.2 From theestimates of these values, the ocean rms azimuth slopes were computed These values aregiven inTable 1.1

Range

Flight direction (azimuth)

Study − site box (512
512)

Wave direction (306 ⴗ )

Pacific Ocean

Northern California

N

Gualala River

FIGURE 1.1 (See color insert following page 240.)

An L-band, VV-pol, AIRSAR image, of northern California coastal waters (Gualala River dataset), showing ocean waves propagating through a study-site box.

Polarimetric SAR Techniques for Remote Sensing of the Ocean Surface 7

Incidence plane H

V

Radar

(Azimuth)

Tilted ocean resolution cell

(Ground range) (Surface normal)

1.2.5 Two-Scale Ocean-Scattering Model: Effect on the Orientation Angle Measurement

In Section 1.2.3.2, Equation 1.5 is given for the orientation angle This equation gives theorientation angle u as a function of three terms from the polarimetric coherency matrix T.Scattering has only been considered as occurring from a slightly rough, tilted surfaceequal to or greater than the size of the radar resolution cell (seeFigure 1.2) The surface isplanar and has a single tilt us This section examines the effects of having a distribution ofazimuth tilts, p (w), within the resolution cell, rather than a single averaged tilt

For single-look or multi-look processed data, the coherency matrix is defined as

We now follow the approach of Cloude and Pottier [23] The composite surface consists offlat, slightly rough ‘‘facets,’’ which are tilted in the azimuth direction with a distribution of tilts,p(w):

p(w) ¼

1 2b jw
sj  b

0 otherwise



(1:7)

where s is the average surface azimuth tilt of the entire radar resolution cell

The effect on T of having both (1) a mean bias azimuthal tilt usand (2) a distribution

of azimuthal tilts b has been calculated in Ref [22] as

T ¼

A B sin c(2b) cos 2us
B sin c(2b) sin 2us

B* sin c(2b) cos 2us 2C( sin22usþ sin c(4b) cos 4us) C(1
2 sin c(4b)) sin 4us

B* sin c(2b) sin 2us C(1
2 sin c(4b)) sin 4us 2C( cos22us
sin c(4b) cos 4us)

2

4

35(1:8)

where sin c(x) is ¼ sin(x)/x and

A ¼ Sj HHþ SVVj2, B ¼ (SHHþ SVV)(S*HH
S*VV), C ¼ 0:5 Sj HH
SVVj2

Equation 1.8 reveals the changes due to the tilt distribution (b) and bias (us) that occur inall terms, except in the term A ¼ jSHHþ SVVj2, which is roll-invariant In the correspond-ing expression for the orientation angle, all of the other terms, except the denominatorterm hjSHH
SVVj2i, are modified

u¼ Arg(hSRRS*LLi) ¼ tan
1
4Re h(SHH
SVV)S*HVi

FIGURE 1.4 (See color insert following page 240.)

Orientation angle spectra versus wave number for azimuth direction waves propagating through the study site The white rings correspond to 50, 100, 150, and 200 m The dominant wave, of wavelength 157 m, is propagating

at a heading of 3068.

1.2.6 Alpha Parameter Measurement of Range Slopes

A second measurement technique is needed to remotely sense waves that have significantpropagation direction components in the range direction The technique must be moresensitive than current intensity-based techniques that depend on tilt and hydrodynamicmodulations Physically based POLSAR measurements of ocean slopes in the rangedirection are achieved using a technique involving the ‘‘alpha’’ parameter of theCloude–Pottier polarimetric decomposition theorem [23]

1.2.6.1 Cloude–Pottier Decomposition Theorem and the Alpha Parameter

The Cloude–Pottier entropy, anisotropy, and the alpha polarization decomposition orem [23] introduce a new parameterization of the eigenvectors of the 3  3 averagedcoherency matrix hjTji in the form

the-L-band orientation angle wave spectra 0.50

Polarimetric SAR Techniques for Remote Sensing of the Ocean Surface 11

35 [U3]*T (1:10)where

[U3] ¼ ejf

cos a1 cos a2ejf2 cos a3ejf3

sin a1cos b1ejd1 sin a2cos b2ejd2 sin a3cos b3ejd3

sin a1sin b1ejg1 sin a2sin b2ejg2 sin a3sin b3ejg3

24

Pi¼Pj¼3lij¼1lj

The individual alphas are for the three eigenvectors and the Ps are the probabilitiesdefined with respect to the eigenvalues In this method, the average alpha is used and is,for simplicity, defined as 
 a For the ocean backscatter, the contributions to theaverage alpha are dominated, however, by the first eigenvalue or eigenvector term.The alpha parameter, developed from the Cloude–Pottier polarimetric scatteringdecomposition theorem [23], has desirable directional measurement properties It is(1) roll-invariant in the azimuth direction and (2) in the range direction, it is highlysensitive to wave-induced modulations of f in the local incidence angle f Thus, the

TABLE 1.1

Northern California: Gualala Coastal Results

In Situ Measurement Instrument Parameter

Bodega Bay, CA 3-m Discus Buoy 46013

Point Arena, CA Wind Station

Orientation Angle Method

Alpha Angle Method Dominant wave

period (s)

wave number

10.2 From dominant wave number Dominant

wavelength (m)

156 From period, depth

spectra

162 From wave spectra Dominant wave

direction (8)

320 Est from wind direction

284 Est from wind direction

306 From wave spectra

306 From wave spectra rms slopes azimuth

slope, wave number

1.92 Est from rms slope, wave number Date: 7/15/94; data start time (UTC): 20:04:44 (BB, PA), 20:02:98 (AIRSAR); wind speed: 1.0 m/s (BB), 2.9 m/s (PA) Mean ¼ 1.95 m/s; wind direction: 3208 (BB), 2848 (PA), mean ¼ 3028; Buoy: ‘‘Bodega Bay’’ (46013) ¼ BB; location: 38.23 N 123.33 W; water depth: 122.5 m; wind station: ‘‘Point Arena’’ (PTAC – 1) ¼ PA; location: 38.968

N, 123.74 W; study-site location: 38839.6 0 N, 123835.8 0 W.