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A Study of the Design and Real-Time Wavelet Transform A STUDY OF THE DESIGN AND REAL-TIME IMPLEMENTATION OF A SEMI-GENERIC INTEGER-TO-INTEGER DISCRETE WAVELET TRANSFORM A Thesis Submitted to the Engineering School of the UNIVERSITY OF DAYTON In Partial Fulfillment of the Requirements for The Degree Master of Science in Electrical Engineering by Michael P. Flaherty, B.E.E UNIVERSITY OF DAYTON Dayton, Ohio May 2006 A STUDY OF THE DESIGN AND REAL-TIME IMPLEMENTATION OF A SEMI-GENERIC INTEGER-TO-INTEGER DISCRETE WAVELET TRANSFORM APPROVED BY: Dr. Frank A. Sc&frino, Ph.D. Adviser Committee Chairman Electrical &; Computer Engineering Dr. Russell Hardie, Pli.D. /V)r. John Weber, PV.D. Committee Member Committee Member Electrical & Computer Engineering Electrical & Computer Engineering Dr. Donald L. Moon, Ph.D. D^rJJos/ph E. Saliba, Ph.D., P.E. Associate Dean, School of Engineering Dean, School of Engineering ii ABSTRACT A STUDY OF THE DESIGN AND REAL-TIME IMPLEMENTATION OF A SEMI-GENERIC INTEGER-TO-INTEGER DISCRETE WAVELET TRANSFORM Name: Michael P. Flaherty University of Dayton, 2006 Advisor: Dr. Frank A. Scarpino JPEG2000 became an international standard in December of 2000 as the newest and most state of the art still image compression standard available according to the Joint Photographic Experts Group (JPEG). This compression standard is based on the discrete wavelet transform(DWT), instead of the more commonly used discrete cosine transform (DCT) which is part of the original JPEG standard. The result of which has been ever increasing amounts of research in the field of wavelet transforms. This research paper presents a method for the real-time implementation of several types of wavelet transforms including the CDF(9,7) and the LeGall(5,3) transforms which make up the core kernels of the JPEG2000 standard[21]. In this thesis, a forward discrete wavelet transform is designed and implemented on the Vertex 2 Pro package 7 FPGA. It is intended for use in a hardware acceler­ ated JPEG2000 implementation. This implementation would have many potential applications including use in digital cameras, motion JPEG2000 applications, or high altitude surveillance schemes. iii This thesis details a design that effectively uses the designs internal memory to allow for a single read - single write design. The single read - single write capability of this provides much more flexibility. By having to input the data only once, a potential implementor has only to worry about feeding the data to a “black box” in the right order and retrieving the data in the correct order. It also make the design very flexible because no specific memories or memory interfaces have to be used. These features allows a user to incorporate this design without the need to understand the implementation details. IV To Myself.. ...for all of your hard work. v ACKNOWLEDGMENTS I would like to thank anyone and everyone who had to listen to me talk about this for months on end. However, I would especially like to thank the following people. • Dr. Frank Scarpino, PhD: I would like to thank you for all of your guidance over the course of my time in grad school. You have not only given sage advice on academic matters, but provided me with valuable life lessons. • Dr. Russell Hardie, PhD and Dr. John Weber, PhD: Thank you to Dr. Hardie and Dr. Weber for your advice and input on the writing of my thesis and for being on my thesis committee. I know you have busy schedules, so thank you for allowing me to take up some of your valuable time. • Dr. Eric Balster, PhD: I would like to thank you for providing me as much insight, if not more, than my actual advisor, and easily answering as many questions. Thank you for all of your time and patience. • Dave Mundy Thaddeus Marrara: I would like to thank you both for listening to me complain and ask an endless number questions I knew you didn’t know the answer to either, when I wasn’t understanding. And for letting me bounce ideas off of you constantly. • Kerry Hill, A1 Scarpelli, and Rob Ewing: I would like to thank you all, as well as the rest of the researchers and managers at Wright-Patterson Air Force Base, whose financial support and use of their resources made this thesis and my continuing education possible. • B. Jane Flaherty: Thank you to my mother for all of you support throughout my fife. You have given me the opportunities that allowed me to go to grad school and do research like this. Thank you. vi • Kristin Schleppi: Thank you for your infinite patience and support throughout my time in grad­ uate school. You supported me every way possible. Without you pushing me to do better, I probably never would have finished. vii TABLE OF CONTENTS Page Approval ..................................................................................................................... ii Abstract iii Dedication..................................................................................................................... v Acknowledgments ......................................................................................................... vi List of Tables.............................................................................................................. x List of Figures xi Chapters: 1. Introduction........................................................................................................ 1 1.1 Image Compression................................................................................... 1 1.1.1 JPEG Image CompressionStandard ....................................... 4 1.1.2 JPEG2000 Image Compression Standard................................ 4 1.2 Real-Time Implementation .................................................................. 6 1.2.1 Motion JPEG2000 ...................................................................... 6 1.2.2 Cost of Hardware Implementations......................................... 7 1.2.3 Importance.................................................................................. 8 1.3 Innovative Contribution......................................................................... 9 1.4 Thesis Organization............................................................................... 10 2. Wavelet Overview............................................................................................... 11 2.1 The Wavelet Transform......................................................................... 12 2.1.1 The Discrete Wavelet Image Transform ............................... 14 2.2 Benefits of the Wavelet Transform ...................................................... 16 viii 3. Lifting Overview......................... ............................................................... 19 3.1 Origins of Lifting ............................................................ 19 3.2 Benefits of Lifting ............ ..................................................................... 19 3.2.1 Integer-to-Integer Lifting ......................................................... 22 3.3 Deriving Lifting Equivalent Filters...................................................... 22 4. Lifted Wavelet Algorithm ............................................................................... 30 4.1 Overview.................................................................................................. 30 4.2 Implementation......................................................................................... 32 4.2.1 Column Processor...................................................................... 33 4.2.2 Row Processor............................................................................ 36 4.2.3 Symmetric Extensions...................... 39 4.3 Creating Generality ............................................................................... 40 5. Hardware Implementation . ............................................................................ 41 5.1 Synthesis Constraints ............................................................................ 41 5.2 Implementing a Lifting Step.................................................................. 42 5.2.1 Implementing the Column Lifting Step . ............................. 43 5.2.2 Implementing the Row Lifting Step......................................... 44 5.2.3 Semi Generality ......................................................................... 44 5.3 Implementing the Row Processor Memory......................................... 45 5.3.1 MemorySolution ........................................................................... 45 6. Conclusions & Future Work............................................................................. 47 Appendices: A...................................................................................................................................... 50 Bibliography ............................................................................................................... 69 ix LIST OF TABLES Table Page 2.1 Dabchicks Orthogonal Wavelets.................................................................. 16 2.2 LeGall(5,3) & CDF(9,7) Bi-orthogonal Wavelets..................................... 16 4.1 Memory Conservation Examples............................................................... 37 5.1 Synthesis Constraints.................................................................................. 42 x LIST OF FIGURES Figure Page 1.1 A General Image Compression Process................................................... 2 2.1 One MR Level Haar Transform............................................................... 14 2.2 Three MR
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