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Adaptive wavelet compression of imagery. Item Type text; Dissertation-Reproduction (electronic) Authors Kasner, James Henry. Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 03/10/2021 19:36:31 Link to Item http://hdl.handle.net/10150/187390 INFORMATION TO USERS This manuscript .has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissenation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. 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Contact UMI directly to order. UMl A Bell & Howell Information Company 300 North Zeeb Road. Ann Arbor. MI48106·1346 USA 313!761-4700 800:521·0600 ADAPTIVE WAVELET COMPRESSION OF IMAGERY by .Jalllcs Hem,)' Kasller A Dissert.at.ioll Sublllitt.ed to the Facult.y of Lhe DEPAHTMENT OF ELECTlHeAL AND COMPUTER L';NGINEEIUNG III Part.ial Flilfilimellt of t.he Requireillellts For t.he Degree of DOCTOR OF PHILOSOPIlY III t.he Gradllate College TIlE UNIYEHSITY OF AH.lZONA I 99 [) UMI Number: 9620447 UMI Microfonn 9620447 Copyright 1996, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeh Road Ann Arbor, MI 48103 2 THE UNIVERSITY OF ARIZONA 00 GRADUATE COLLEGE As members of the Final Examination Committee, we certify that we have read the dissertation prepared by James Henry Kasner entitled Adaptive Wavelet Compression of Imagery and recommend that it be accepted as fulfilling the dissertation requirement [or the Degr.ee of Doctor of Philosophy 1/-17- C)s- Date 1/-( 7~C;?- Date 11-17--95./ Date Date Date Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. /1-/7- 9S:- Dissertat~on Director Date Michael W. Marcellin 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. 4 ACKNOWLEDGEMENTS It would not have been possible for me to complete this work without the help of many talented people. I would like to thank my advisors Dr. Marcellin and Dr. Hunt for their support, help, insights, and encouragement. Without their contributions, this work would not exist. I also wish to thank Dr. Rodriguez for being kind enough to review this dissertation and offer helpful suggestions. I especially want to thank Ali and Barbie for handling the scheduling and paper work necessary for my defense. It was not an enjoyable task and I appreciate their efforts. I would also like to thank Sriram, Mari, Ke, Dave and Dave, Phil, Wayne, Ed, Jim, Dongchang, and many other graduate students in the ECE department for their friendship and support. Finally I wish to thank my family and parents for their continued confidence, patience, and encouragement. 5 TABLE OF CONTENTS LIST OF FIGURES. 7 LIST OF TABLES. 10 ABSTRACT . ... 11 1 INTRODUCTION 13 2 QUANTIZATION 19 2.1 Introduction .. 19 2.2 Scalar Quantization 21 2.3 Trellis Coded Quantization 35 2.4 Entropy-Constrained Trellis Coded Quantization 41 2.5 Universal Trellis Coded Quantization. 46 3 ENTROPY CODING 52 3.1 Introduction .. , 52 3.2 Huffman Coding 53 3.3 Arithmetic Coding 61 4 WAVELET ANALYSIS/SYNTHESIS 77 4.1 Introduction ........ 77 4.2 Subband Filters ...... 79 4.3 Discrete Wavelet Transform. 82 4.4 Symmetric Extension .... 87 5 ADAPTIVE WAVELET CODERS 96 5.1 Introduction ........... 96 5.2 Recursive Wavelet Analysis/Synthesis 98 5.3 Codebooks and Rate Allocation. 102 5.4 Classification/Adaptive Scan .. 121 5.5 UTCQ Coder . 134 5.6 Comparison With Other Coders 141 6 SUMMARy ...... ...... 146 (i TABLE OF CONTENTS -- Continued Appendix A. FILE FORMATS ..... 1.'iO Appendix B. ORIGINAL IMAGES I:"jl Appendix C. CODED IMAGERY l!i7 REFERENCES ... ........ IG!) 7 LIST OF FIGURES 1.1 Digital Image Communication System . 16 2.1 Uniform Scalar Quantizer Characteristic. 23 2.2 Uniform Scalar Quantizer Characteristic (alternative form) 23 2.3 Distortion-Rate Performance of Scalar Quantizers (Gaussian source) 28 2.4 Granular Gain of TCQ versus Trellis Size . 36 2.5 TCQ Performance for Memoryless Gaussian Source. 37 2.6 Four State Trellis and Codebook Partitioning . 38 2.7 Example Uniform Codebool< for X E [-8,8J at R=2 bits 39 2.8 Example TCQ Codebook for X E [-8, 8J at R=2 bits. 39 2.9 2-D Voronoi Regions for Uniform Codebook ...... 40 2.10 2-D Voronoi Regions for TCQ Codebook (initial state = 0) 41 2.11 2-D Voronoi Regions for TCQ Codebook (ini tial state = 1) 42 2.12 2-D Codewords for TCQ versus Initial Trellis State. 43 2.13 ECTCQ Performance (Memoryless Gaussian Source) 44 2.14 UTCQ Subset Labels ................ 46 2.15 UTCQ Superset Indices ............... 47 2.16 UTCQ Performance (Memoryless Gaussian Source) . 50 2.17 Relative UTCQ Performance (Full Training) . 51 3.1 Tree Structure of Prefix Code. 55 3.2 Construction of First Huffman Code . 59 3.3 Construction of Second Huffman Code 60 3.4 CDF for Source of Table 3.3. 62 3.5 First Arithmetic Encoding Example . 65 3.6 Second Arithmetic Encoding Example 67 3.7 Arithmetic Coder Interval . 69 3.8 Arithmetic Rate vs. Threshold (Gaussian, R = 7.0 bits, ECTCQ) 74 3.9 Optimal Arithmetic Threshold vs. Rate (Gaussian, ECTCQ) .. 75 3.10 Arithmetic/ECTCQ Distortion-Rate Performance (Gaussian) . 76 3.11 Relative Performance Arithmetic/ECTCQ versus Entropy (Gaussian) 76 4.1 Two-band Analysis/Synthesis System . 79 4.2 Multiresolution Analysis and Synthesis. 86 4.3 Example Sequence . 89 4.4 Extension Operators and Signal Symmetries . 90 LIST OF FIGURES - Conti-II/fwd G.l WaVC'iet Ellcodcr alld /)c('oder Diagrams . D7 5.2 lVloclified 1\<Iallal '1'1'('(' ....... 101 5.:1 FiV<' CCIl('rillized-Cilllssiall DCllsiti('s . lOG f).'1 C:cllcl'alized-Ciallssiall 1\" VS. (l 107 G,;") EIlC'rgy W(·ights 1';Xillllplc 1-]) Syst('111 110 G,G lITCQ Bate vs. lop;( -d' ), n = 1.0 IIG !j.7 UTCQ.6 vs. log( -d' ), (\ = 1.0 117 !j.t) Straight !'ill(~ Approxilllatioll II~ 5.9 Jlyperbolic Sect.ioll .... II ~J 5.lO Laplaciall Hate Fit. Error .. 121 rJ.ll Laplacia II .6 Fi t Erl'Or . 122 5.12 Classificatioll PSNR P('rfOl'lIlClIl(,(' for !'(,Illla (ECTCQ) 12G 5.I:J Class Map Propagat.ioll 1'01' .1-lIIap 128 fl. I I Class iVlap Propagat.ioll for :l-Illap 1:11 G.I G !,clllla Class I'l'lap I (HL) 1:12 r).lO L(~lllla Class l'vlap 2 (LH) . , .. , 1:12 G.17 L<'lllla Class 1'\'lap :1 (I-II-I) ..... 1:1:1 G.IS I'SNR Figlll'('s 1'01' Codillg GI2 X GI2 !'<'Illla II :) /\.1 ECTCQ Coder I"ile FOl'lllat. /\.2 UTCQ Coder File· FOl'lllaL . 13.1 Chest. Illlclgc (102·1 X 102·l) IGl 11.2 /\('rial Illlag<' (102,1 X ID2·1) 1 Sri 13.:1 L('llllil Illwge (!j12 X 512) lSG n.1 :1 Level De('ompositioll . ISCi l!.ri l\·JH.1 IlIIage (G 12 X rJ 12) IS() jfi(i lUi S/\It IllIage (S12 X ri12) C.I I~CTCQ, 1101l-adc1pt., 0.25 bpp . 158 C.2 ECTCQ, II-Map, 0.25 bpp . " ISS C.:l I';CTCQ, :l-Map, n.2G bpp .. lSS C.ll ECTCQ, lloll-adapt., 0.5 bpi> 159 C.S ECTCQ, .1-Map, O.S bpp .. 159 (:.fi ECTCQ, :l-Map, 0.5 bpp .. lri9 C.7 UTCq, lloll-adapt., 0.25 hpi> . IGO Co8 l JTCQ, Iloll-adapt., D.S bpp IGO (:.9 UTCQ, adapt, 0.25 bpp , , " IGO LIST OF FIGURES - Conti'll:ned C.IO UTCQ, adapt., OJi hpp ..

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