Two Dimensional Phase Unwrapping-Theory Algorithms and Software

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Two Dimensional Phase Unwrapping-Theory Algorithms and Software。二维相位解缠绕,该书囊括目前用于干涉相位解缠绕的几乎所有主流方法,是解缠书籍中的经典,可作为重要的参考书或工具书。
The image shown on the radar interfero erences between the complex valued be unwrapped. This is a difficult phase e wraps very quickly and disturbances that occurred between the two passes. which were 24 days apar. also corrupt the phase. This imag for the Terrain Modeling Project funded by the Det Engineering Center, The SaR data was providied by Radarsat lnternational inter ferogran was generated and provided by Vexcel Corporation, Boulder. Ce D00 Copyright t 1998 by John wiley Sons, Inc. All rights reserved mechanical photocopying. recording, scat states Copyright Act, without either the prior written permissio of the Publisher, or authorization through payment of the Rosewood Drive, Danvers, MA 01923, (978)750-8400 fax (978) 750-4744. Requests to the Publisher for pemission should be addressed to the Permissions Department, John wiley & st nc.. 605 Third Avenue, New York, NY 10158-0012(212)850- 6011,fax(212)850-6008.E-Mail:PERMREQ@WILEY.COM Library of Congress Cataloging in Publication Data Dennis C wo-dimensional phase unwrapping: theory, algorithms, and ware/Dennis C Ghiglia and Mark D. Pritt Includes bibliographical references and index ISBN 0-471-24935-1(cloth: alk. paper I. Synthetic aperture radar. 2. Signal processing--Mathematics .Prit. Mark D.Ⅱ Title. TK6592S95G451998 621.367-dc21 97-38034 Printed in the United States of America 10987654321 oA!i7:iii( FOREWORD Two-dimensional phase unwrapping is the type of problem that is typically the domain of the mathematician. It is both complex and abstract. However, phase unwrapping is also the core technology that enables radar interferometry Over the past decade interferometry has changed the way that we use radar data. Radar data are now used for precise measurement of surface topography in clouded regions. Additionally, spaceborne radar systems have proved effective for measuring surface changes from earthquakes and volcanic eruptions. These applications have created a new class of radar data users primarily involved in mapping and remote sensing applications In Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software the authors unlock the mystery of phase unwrapping in interferometric data processing. This text provides a clear, concise treatment of phase unwrapping that cannot be found in any other source. It presents for the first time the relationship between theory and application. Its uniform treatment of the various phase unwrapping techniques makes it a valuable resource for any engineer or scientist involved in processing or exploitation of interferometric data I expect that radar interferometry will increase in importance over the coming decade with the development of airborne and spaceborne sensor systems designed to optimally exploit this tcchnology. Two-Dimensional Phase Unwrap ping: Theory, Algorithms, and Software is an important contribution to ot nderstanding of radar interferometry that will bencfit both research into advanced techniques and the design of these future sensor systems JOHN C. CURLANDER President and CEO Vexcel Corpore PREFACE wo-dimensional phase unwrapping arises most naturally in, but is not restricted to, interferometric applications. Measured or calculated phase values from two or more mutually coherent multidimensional signals are related in a nonlinear manner to a desired physical quantity of interest. The nonlinearity is in the form of"wraps"or cycle discontinuities where an underlying two- dimensional phase is wrapped into the interval (T, 7. The wrapped phase must somehow be unwrapped in order to provide an estimate of the underlying physical quantity. Estimation of surface topography from interferometric synthetic aperture radar(SAR)or extremely accurate profiling of mechanical parts by optical interferometers are two such examples Originally developed for military reconnaissance, SAR is now experiencing new life in civil applications. In fact civilian and commercial interests are rapidly becoming the drivers of technology. Clever utilization of the coherent SAR imagery in interferometric configurations makes possible the measurement of surface topography to accuracies much better than the spatial resolution(0.3 meters to several meters)of the SAR images themselves. Indeed, as is common lace with interferometers measurement sensitivities are on the order of the operating wavelength, which is typically a few centimeters for SAR. Imaging geometries, noise, and other operational factors degrade performance some- what from centimeter-scale accuracies, but nevertheless SAR interferometry makes possible global topographic mapping in a timely fashion, in daylight or at night, in all weather conditions, and with unprecedented accuracy. SAR interferometry also can detect deformations of the carth's crust on the order of millimeters ability that shows promise for the timely detection of nic These exciting possibilities have led to an explosive growth in the field of phase inwrapping as indicated by the increasing number of journal publications Newcomers to SAR interferometry and related disciplines will eventually confront the phase unwrapping problem and, undoubtedly, will rather bewildering variety of ideas and algorithms, including those based on neural networks, simulated annealing, cellular automata, genetic algorithms, and other unusual constructs. Which of these are good? Which are not? We do Throughout this book we use the notation(-丌,n] to represent the interval-丌<x≤丌 not have complete answers to these questions, and in all likelihood there never will be a complete answer. However, we can help researchers approach the probler the context of their own applications with some guidance from those who have been through the school of hard knocks We have greatly simplified the investigative process by categorizing phase unwrapping approaches into two general classes: path-following and minimum- norm methods. We have provided detailed descriptions and analyses of four path-following approaches and four minimum-norm approaches. As is the case with politics, there are plenty of partisan participants firmly entrenched in their own camp with nary a nod of recognition to an opposing view. We ourselves are uilty of this to some degree. However, we provide enough theory, philosophy, algorithms, and references to allow researchers to make up their own minds in a ch more timely fashion than if sifting had one. Fortunately, unlike politics, sound scientific investigation makes it easier to switch"party affiliations"if necessary While this book is slanted toward SAR interferometry applications, it has much in common with other disciplines in which phase unwrapping plays an important role. In fact it is safe to say that the phase unwrapping problems ncountered in SAR are about"as hard as they come. "Practical solutions for SAR interferometry should easily find a place in related applications outside the field of SAR. We believe readers of this book will have no trouble bridging the gap. This book provides another useful function. Most researchers are"quick studies"and soon learn which algorithms they would like to try. Newcomers usually lack the basic building blocks of operational codes from which timely sults spring forth. as we all know, it takes time to develop and successfully implement a working algorithm. To this end, we have supplied a suite of c language programs and routines comprising over 6000 lines of source code that implement the ideas and algorithms discussed in this book. We have already done the laborious part of coding the algorithms, fixing the bugs, and contacting the authors of the algorithms to discover thetricks "necessary to get them to work correctly. We encourage the reader to understand how the algorithms work, use them properly, modify them as appropriate, and improve them. These ograms, which are listed in Appendix A, are available for downloading on the Wiley ftp server, along with a number of phase unwrapping datasets. See Appendix C for details The supplied software comprises only a subset of the vast suite of published and unpublished algorithms. We have selected and implemented those that we believe are representative of the current"state-of-the-art"in phase unwrapping such as Flynn's minimum discontinuity algorithm, while not neglecting the older and more"classic"algorithms, such as the residue and branch cut algorithm of Goldstein. Zebker, and Werner. Omissions of certain algorithms are not a suggestion of inadequacy. We just could not include them all. By contrast PREFACE nclusion is not a claim of superiority. Instead, they should be viewed for the insight and perspective they provide. Indeed new and potentially powerful and seful algorithms are being developed all the time. This is the sign of a vital and dynamic field, and we should be encouraged rather than befuddled Many of the ideas, concepts, philosophies, and algorithms discussed are not, of course, our own. We have been fortunate to work with many talented olleagues who have helped us immensely for many years in many divers ways.Assistance has come in the form of developing challenging problems providing experimental data, offering first-rate mathematical and algorithmic ssistance, supplying hardware and software support, and providing a stimulat- ing and supportive work environment. For all of these reasons and more we wish to extend sincere thanks to Charles V. Jakowatz, Jr, Louis A. Romero, Gary A Mastin, Daniel E. Wahl, Paul A. Thompson, Bruce C. Walker, william H Hensley, David K. Johnson, Terry M. Calloway, Terry A Bacon, Michael J Roth and edward J. Nowicki We especially wish to thank Thomas J. Flynn, Paul H. Eichel, and Doug L. Bickel of Sandia National Laboratories for their thorough and insightful reviews of this book. Tom Flynn was especially helpful with his collaboration during the preparation of this work and the actual research investigations. He developed one of the phase unwrapping codes, and he graciously allowed us to present and distribute it to the research community. Michael J. Roth of the Johns Hopkins University Applied Physics Laboratory supplied us with two phase wrapping examples that were generated by his IFSAR simulator. In addition Richard M. Goldstein of the Jet Propulsion Laboratory provided invaluable assistance with our understanding of the subtleties of the widely used algorithm credited to him and his colleagues, Howard A. Zebker and Charles L. Werner. Finally we wish to thank John C. Curlander of Vexcel Corporation for writing the forewor This work was performed in part at Sandia National Laboratories, Albu querque, NM. Sandia is a multiprogram laboratory operated by Sandia Cor- poration, a Lockheed Martin company, for the United States Department of Energy under Contract DE-AC04-94AL85000 Dennis C. Ghiglia would like to express his thanks and appreciation to the management of Sandia National Laboratories and the U.S. Department of Energy for their support throughout his career. He also wishes to thank his son Daniel C. Ghiglia, for his expertise and invaluable assistance with the artwork development and LATEX typesetting, and his wife Ruth Ann and daughter Carla for their understanding and support during the time-consuming process of book writing Mark D. Pritt would like to express his thanks and appreciation to Hal Garner, a vice president of Lockheed Martin Corporation, for funding the research and writing of this book. He also wishes to thank his former manager, Sharon L. Smith, for her invaluable support of this effort, and his current REFACE manager, Rick w. Duke, for helping bring it to completion. Last, but certainly not least, he wishes to thank his wife christine and his chiidren anna, Jacob Emily, Samuel, and Noah for their enthusiastic support and encouragement MARK D, PRITT Lockheed Martin Corporation CONTENTS Foreword Preface 1 Introduction to phase Unwrapping 1. 1 The Importance of Phase/I 1. 2 The Need for Phase Unwrapping/4 1.3 Aspects of One-Dimensional Phase Unwrapping /16 1. 4 Summary and Brief Look Ahead/ 26 References /28 2 Line Integrals, Residues, and 2-D Phase Unwrapping 2. 1 Introduction/31 2.2 Differential Forms and Conditions for Path Independence /32 2.3 Theory of Residues and Applications to Phase Unwrapping /39 2.4 Phase Decomposition into"Irrotational"and"Rotational Components /43 2.5 Discrete Formulation of Two-Dimensional Phase Unwrapping/44 6 Simple Tests for Path Dependence /46 2.7 Residues, Gradients, and Phase Decomposition: Examples /50 2.8 Conclusion /54 References 3 Phase Data, Quality Maps, Masks, and Filters 3. 1 Introduction /59 3.2 Phase Data Examples /59 3.3 Quality Maps/70 3.4 Masks 3.5 Noise Filtering/90 3.6 Summary and Conclusion /9 References /98 4 Path-Following Methods 4.1 Introduction/10 4.2 Goldstein's Branch Cut Algorithm /103 4.3 Quality-Guided Path F ollowing /122 4.4 Mask Cut Algorithm /136 4.5 Flynn's Minimum Discontinuity Approach /151 4.6 Summary and Conclusion /172 References /176 5.1 Introduction /178 5.2 Mimimum LP-Norm Formulation/ 181 5.3 Unweighted Least-Squares Phase Unwrapping /188 5.4 Weighted Least-Squares Phase Unwrapping /215 5.5 Minimum LP-Norm Phase Unwrapping/ 248 5.6 Summary and Conclusion /273 References /277 6 Comparisons and conclusion 6.1 Comparisons of Phase Unwrapping Algorithms/280 6.2 Links Between Path-Following and Minimum-Norm Algorithms /288 6.3 Measures of Success/293 6.4 Future Directions /306 6.5 Conclusion/308 References /309

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