WAVELET IMAGE AND VIDEO COMPRESSION Contents 1 Introduction by Pankaj N Topiwala Background Compression Standards Fourier versus Wavelets Overview of Book 4.1 Part I: Background Material 4.2 Part II: Still Image Coding Part III: Special Topics in Still Image Coding 4.3 4.4 Part IV: Video Coding References 10 11 12 I Preliminaries 13 Preliminaries by Pankaj N Topiwala Mathematical Preliminaries 1.1 Finite-Dimensional Vector Spaces Analysis 1.2 Fourier Analysis 1.3 Digital Signal Processing Digital Filters 2.1 2.2 Z-Transform and Bandpass Filtering Primer on Probability References 15 15 15 19 21 23 24 25 28 30 Time-Frequency Analysis, Wavelets And Filter Banks by Pankaj N Topiwala Fourier Transform and the Uncertainty Principle Fourier Series, Time-Frequency Localization 2.1 Fourier Series Time-Frequency Representations 2.2 The Continuous Wavelet Transform Wavelet Bases and Multiresolution Analysis Wavelets and Subband Filter Banks Two-Channel Filter Banks 5.1 5.2 Example FIR PR QMF Banks Wavelet Packets References 33 33 38 38 40 43 45 51 51 56 57 58 4 7 Contents vi Introduction To Compression by Pankaj N Topiwala Types of Compression Resume of Lossless Compression DPCM 2.1 2.2 Huffman Coding 2.3 Arithmetic Coding 2.4 Run-Length Coding Quantization Scalar Quantization 3.1 3.2 Vector Quantization 61 63 64 64 66 66 67 68 70 70 73 73 73 73 75 76 78 79 79 80 Summary of Rate-Distortion Theory 61 Image Quality Metrics Metrics 6.1 Approaches to Lossy Compression VQ 5.1 5.2 Transform Image Coding Paradigm JPEG 5.3 5.4 Pyramid 5.5 Wavelets 6.2 Human Visual System Metrics References Symmetric Extension Transforms by Christopher M 83 Brislawn 83 Expansive vs nonexpansive transforms 85 Four types of symmetry 86 Nonexpansive two-channel SET’s References 91 II 93 Still Image Coding Wavelet Still Image Coding: A Baseline MSE and HVS Approach 95 95 96 97 101 103 105 106 by Pankaj N Topiwala Introduction Subband Coding (Sub)optimal Quantization Interband Decorrelation, Texture Suppression Human Visual System Quantization Summary References Image Coding Using Multiplier-Free Filter Banks by Alen Docef, Faouzi Kossentini, Wilson C Chung and Mark J T Smith Introduction 1 111 111 Based on “Multiplication-Free Subband Coding of Color Images”, by Docef, Kossentini, Chung and Smith, which appeared in the Proceedings of the Data Compression Contents Coding System Design Algorithm vii 112 114 116 117 119 Multiplierless Filter Banks Performance References Embedded Image Coding Using Zerotrees of Wavelet Coefficients by Jerome M Shapiro 123 Introduction and Problem Statement 123 Embedded Coding 124 1.1 1.2 Features of the Embedded Coder 124 1.3 Paper Organization 125 Wavelet Theory and Multiresolution Analysis 125 2.1 Trends and Anomalies 125 2.2 Relevance to Image Coding 126 2.3 A Discrete Wavelet Transform 127 Zerotrees of Wavelet Coefficients 128 3.1 Significance Map Encoding 128 3.2 Compression of Significance Maps using Zerotrees of Wavelet Coefficients 130 3.3 Interpretation as a Simple Image Model 132 3.4 Zerotree-like Structures in Other Subband Configurations 135 Successive-Approximation 135 4.1 Successive-Approximation Entropy-Coded Quantization 136 4.2 Relationship to Bit Plane Encoding 137 4.3 Advantage of Small Alphabets for Adaptive Arithmetic Coding 138 4.4 Order of Importance of the Bits 139 4.5 Relationship to Priority-Position Coding 140 A Simple Example 141 Experimental Results 143 Conclusion 146 References 146 A New Fast/Efficient Image Codec Based on Set Partitioning in Hierarchical Trees by Amir Said and William A Pearlman 157 Introduction 157 Progressive Image Transmission 159 Transmission of the Coefficient Values 160 Set Partitioning Sorting Algorithm 161 Spatial Orientation Trees 162 Coding Algorithm 163 Numerical Results 165 Summary and Conclusions 168 References 168 Conference, Snowbird, Utah, March 1995, pp 352-361, ©1995 IEEE Contents viii 10 Space-frequency Quantization for Wavelet Image Coding by Zixiang Xiong, Kannan Ramchandran, and Michael T Orchard 171 Introduction 171 Background and Problem Statement 173 Defining the tree 173 2.1 Motivation and high level description 173 2.2 Notation and problem statement 174 2.3 Proposed approach 176 2.4 The SFQ Coding Algorithm 177 Tree pruning algorithm: Phase I (for fixed quantizer q and 3.1 fixed ) 177 Predicting the tree: Phase II 181 3.2 Joint Optimization of Space-Frequency Quantizers 183 3.3 Complexity of the SFQ algorithm 184 3.4 Coding Results 184 Extension of the SFQ Algorithm from Wavelet to Wavelet Packets 185 Wavelet packets 187 Wavelet packet SFQ 188 Wavelet packet SFQ coder design 189 Optimal design: Joint application of the single tree algorithm 8.1 and SFQ 190 Fast heuristic: Sequential applications of the single tree algo8.2 rithm and SFQ 190 Experimental Results 191 Results from the joint wavelet packet transform and SFQ design 191 9.1 9.2 Results from the sequential wavelet packet transform and SFQ design 191 10 Discussion and Conclusions 192 11 References 194 11 Subband Coding of Images Using Classification and Trellis Coded Quantization by Rajan Joshi and Thomas R Fischer 199 Introduction 199 Classification of blocks of an image subband 199 Classification gain for a single subband 200 2.1 Subband classification gain 202 2.2 Non-uniform classification 202 2.3 The trade-off between the side rate and the classification gain 203 2.4 Arithmetic coded trellis coded quantization 204 Trellis coded quantization 206 3.1 Arithmetic coding 208 3.2 Encoding generalized Gaussian sources with ACTCQ system 209 3.3 Image subband coder based on classification and ACTCQ 211 Description of the image subband coder 212 4.1 Simulation results 214 Acknowledgment 215 References 215 Contents ix 12 Low-Complexity Compression of Run Length Coded Image Subbands by John D Villasenor and Jiangtao Wen 221 Introduction 221 III Large-scale statistics of run-length coded subbands 222 Structured code trees Code Descriptions 3.1 3.2 Code Efficiency for Ideal Sources Application to image coding Image coding results Conclusions References Special Topics in Still Image Coding 224 224 227 229 232 233 234 237 13 Fractal Image Coding as Cross-Scale Wavelet Coefficient Prediction by Geoffrey Davis 239 Introduction 239 Fractal Block Coders 239 Motivation for Fractal Coding 2.1 2.2 Mechanics of Fractal Block Coding Decoding Fractal Coded Images 2.3 A Wavelet Framework 240 240 242 243 Notation 243 3.1 A Wavelet Analog of Fractal Block Coding 243 3.2 Self-Quantization of Subtrees 245 4.1 Generalization to non-Haar bases 245 4.2 Fractal Block Coding of Textures 246 Implementation 246 5.1 Bit Allocation 246 Results 247 SQS vs Fractal Block Coders 247 6.1 6.2 Zerotrees 249 6.3 Limitations of Fractal Coding 250 References 251 14 Region of Interest Compression In Subband Coding by Pankaj N Topiwala Introduction Error Penetration Quantization Simulations Acknowledgements References 253 253 254 255 256 257 258 15 Wavelet-Based Embedded Multispectral Image Compression by Pankaj N Topiwala 261 Introduction 261 Contents x An Embedded Multispectral Image Coder 2.1 Algorithm Overview 2.2 Transforms 2.3 Quantization 2.4 Entropy Coding Simulations References 262 263 265 265 266 267 268 16 The FBI Fingerprint Image Compression Specification by Christopher M Brislawn Introduction 1.1 Background 1.2 Overview of the algorithm The DWT subband decomposition for fingerprints 2.1 Linear phase filter banks 2.2 Symmetric boundary conditions 2.3 Spatial frequency decomposition Uniform scalar quantization 3.1 Quantizer characteristics Bit allocation 3.2 Huffman coding 4.1 The Huffman coding model 4.2 Adaptive Huffman codebook construction The first-generation fingerprint image encoder 5.1 Source image normalization 5.2 First-generation wavelet filters Optimal bit allocation and quantizer design 5.3 Huffman coding blocks 5.4 Conclusions 271 271 272 275 276 276 277 278 280 280 281 281 281 282 283 283 283 283 286 286 287 References 17 Embedded Image Coding Using Wavelet Difference Reduction by Jun Tian and Raymond O Wells, Jr Introduction Discrete Wavelet Transform Differential Coding Binary Reduction Description of the Algorithm Experimental Results SAR Image Compression Conclusions References 289 289 290 291 291 292 294 295 296 300 18 Block Transforms in Progressive Image Coding by Trac 303 D Tran and Truong Q Nguyen Introduction 303 The wavelet transform and progressive image transmission 304 Wavelet and block transform analogy 305 Contents xi 307 Coding Results 308 References 313 Transform Design IV Video Coding 317 19 Brief on Video Coding Standards by Pankaj N Topiwala Introduction H.261 MPEG-1 MPEG-2 H.263 and MPEG-4 References 319 319 319 320 321 321 322 20 Interpolative Multiresolution Coding of Advanced TV with Subchannels by K Metin Uz, Didier J LeGall and Martin 323 Vetterli Introduction2 323 Multiresolution Signal Representations for Coding 325 Subband and Pyramid Coding 326 3.1 Characteristics of Subband Schemes 3.2 Pyramid Coding Analysis of Quantization Noise 327 328 3.3 329 The Spatiotemporal Pyramid 330 Multiresolution Motion Estimation and Interpolation 333 Basic Search Procedure 334 5.1 5.2 Stepwise Refinement 335 Motion Based Interpolation 336 5.3 Compression for ATV 337 Compatibility and Scan Formats 338 6.1 Results 339 6.2 Relation to Emerging Video Coding Standards 341 6.3 Complexity 342 Computational Complexity 342 7.1 Memory Requirement 343 7.2 Conclusion and Directions 343 References 344 21 Subband Video Coding for Low to High Rate Applications by Wilson C Chung, Faouzi Kossentini and Mark J T Smith 349 Introduction 349 ©1991 IEEE Reprinted, with permission, from IEEE Transactions of Circuits and Systems for Video Technology, pp.86-99, March, 1991 Based on “A New Approach to Scalable Video Coding”, by Chung, Kossentini and Smith, which appeared in the Proceedings of the Data Compression Conference, Snowbird, Utah, March 1995, ©1995 IEEE Contents Basic Structure of the Coder Practical Design & Implementation Issues Performance References xii 350 354 355 357 22 Very Low Bit Rate Video Coding Based on Matching Pursuits by Ralph Neff and Avideh Zakhor Introduction Matching Pursuit Theory Detailed System Description 3.1 Motion Compensation 3.2 Matching-Pursuit Residual Coding 3.3 Buffer Regulation 3.4 Intraframe Coding Results Conclusions References 23 Object-Based Subband/Wavelet Video Compression by Soo-Chul Han and John W Woods Introduction Joint Motion Estimation and Segmentation 2.1 Problem formulation 2.2 Probability models Solution 2.3 Results 2.4 Parametric Representation of Dense Object Motion Field 3.1 Parametric motion of objects 3.2 Appearance of new regions 3.3 Coding the object boundaries Object Interior Coding 4.1 Adaptive Motion-Compensated Coding 4.2 Spatiotemporal (3-D) Coding of Objects Simulation results Conclusions References 361 361 362 364 364 365 373 374 374 379 381 383 383 384 385 385 387 387 389 389 391 391 391 392 392 393 395 395 24 Embedded Video Subband Coding with 3D SPIHT by 397 William A Pearlman, Beong-Jo Kim, and Zixiang Xiong Introduction 398 System Overview 400 System Configuration 400 2.1 3D Subband Structure 400 2.2 SPIHT 402 3D SPIHT and Some Attributes 403 4.1 Spatio-temporal Orientation Trees 404 4.2 Color Video Coding 407 4.3 Scalability of SPIHT image/video Coder 408 24 Embedded Video Subband Coding with 3D SPIHT 424 [21] J M Shapiro An Embedded Wavelet Hierarchical Image Coder Proceedings IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), San Francisco, pages IV 657–660, March 1992 [22] P G Sherwood and K Zeger Progressive Image Coding for Noisy Channels IEEE Signal Processing Letters, 4(7):189–191, July 1997 [23] D Taubman Directionality and Scalability in Image and Video Compression PhD thesis, University of California, Berkeley, 1994 [24] D Taubman and A Zakhor Multirate 3-D Subband Coding of Video IEEE Transactions on Image Processing, 3(5):572–588, Sep 1994 [25] A M Tekalp Digital Video Processing Prentice Hall, Inc, 1995 [26] J Y Tham, S Ranganath, and A A Kassim Highly Scalable Wavelet-Based Video Codec for Very Low Bit-rate Environment To appear in IEEE Journal on Selected Area in Communications, 1998 [27] I H Witten, R M Neal, and J G Cleary Arithmetic Coding for Data Compression Communications of the ACM, 30(6):520–540, June 1987 [28] Z Xiong, K Ramchandran, and M T Orchard Wavelet Packet Image Coding Using Space-Frequency Quantization Submitted to IEEE Transactions on Image Processing, 1996 [29] Z Xiong, K Ramchandran, and M T Orchard Space-Frequency Quantization for Wavelet Image Coding IEEE Transactions on Image Processing, 6:677–693, May 1997 425 FIGURE 14 Comparison of visual performance of 3-D SPIHT with (middle), and MPEG-2 (bottom) at bit-rate of 0.2 bpp (top), 24 Embedded Video Subband Coding with 3D SPIHT 426 FIGURE 15 Frame-by-frame PSNR comparison of 3D SPIHT, MC 3D SPIHT, and H.263 at 30 and 60 kbps and 10 fps with “Carphone” sequence 24 Embedded Video Subband Coding with 3D SPIHT 427 FIGURE 16 Frame-by-frame PSNR comparison of 3D SPIHT, MC 3D SPIHT, and H.263 at 30 and 60 kbps and 10 fps with “Mother and Daughter” sequence 24 Embedded Video Subband Coding with 3D SPIHT 428 FIGURE 17 Frame-by-frame PSNR comparison of 3D SPIHT, MC 3D SPIHT, and H.263 at 30 and 60 kbps and 10 fps with “Hall Monitor” sequence 24 Embedded Video Subband Coding with 3D SPIHT 429 FIGURE 18 The same reconstructed frames at 30 kbps and 10 fps (a)Top-left: original “Carphone” frame 198 (b)Top-right: H.263 (c)Bottom-left: 3D SPIHT (d)Bottom-right: MC 3D SPIHT 24 Embedded Video Subband Coding with 3D SPIHT 430 FIGURE 19 The same reconstructed frames at 30 kbps and 10 fps (a)Top-left: original “Mother and Daughter” frame 102 (b)Top-right: H.263 (c)Bottom-left: 3D SPIHT (d)Bottom-right: MC 3D SPIHT 24 Embedded Video Subband Coding with 3D SPIHT 431 FIGURE 20 The same reconstructed frames at 30 kbps and 10 fps (a)Top-left: original “Hall Monitor” frame 123 (b)Top-right: H.263 (c)Bottom-left: 3D SPIHT (d)Bottom-right: MC 3D SPIHT 24 Embedded Video Subband Coding with 3D SPIHT 432 FIGURE 21 Multiresolutional decoded frame of “Carphone” sequence with the embedded 3D SPIHT video coder (a)Top-left: spatial half resolution (88 x 72 and 10 fps) (b)Top-right: spatial and temporal half resolution ( and fps) (c)Bottom-left: temporal half resolution ( and fps) (d)Bottom-right: full resolution ( and 10 fps) Appendix A Wavelet Image and Video Compression — The Home Page Pankaj N Topiwala Homepage For This Book Since this is a book on the state of the art in image processing, we are especially aware that no mass publication of the digital images produced by our algorithms could adequately represent them That is why we are setting up a home page for this book at the publishers’ site This home page will carry the actual digital images and video sequences produced by the host of algorithms considered in this volume, giving direct access for comparision with a variety of other methodologies Look for it at http://www.wkap.com Other Web Resources We’d like to list just a few useful web resources for wavelets and image/video compression Note that these lead to many more links, effectively covering these topics www.icsl.ucla.edu/ ipl/psnr_results.htm Extensive compression PSNR results ipl.rpi.edu:80/SPIHT/ Home page of the SPIHT coder, as discussed in the book www.cs.dartmouth.edu/ gdavis/wavelet/wavelet.html Wavelet image compression toolkit, as discussed in the book links.uwaterloo.ca/bragzone.base.html A compression brag zone www.mat.sbg.ac.at/ uhl/wav.html A compendium of links on wavelets and compression www.mathsoft.com/wavelets.html A directory of wavelet papers by topic www.wavelet.org Home page of the Wavelet Digest, an on-line newsletter www.c3.lanl.gov/ brislawn/FBI/FBI.html Home page for the FBI Fingerprint Compression Standard, as discussed in the book www-video.eecs.berkeley.edu/ falcon/MP/mp_intro.html Home page of the matching pursuit video coding effort, as discussed in the book 434 10 saigon.ece.wisc.edu/ waveweb/QMF.html Homepage of the Wisconsin wavelet group, as discussed in the book 11 www.amara.com/current/wavelet.html A compendium of wavelet resources Appendix B The Authors Pankaj N Topiwala is with the Signal Processing Center of Sanders, A Lockheed Martin Company, in Nashua, NH pnt@sanders.com Christopher M Brislawn is with the Computer Research and Applications Division of the Los Alamos National Laboratory, Los Alamos, NM brislawn@lanl.gov Alen Docef, Faouzi Kossentini, and Wilson C Chung are with the School of Engineering, and Mark J T Smith is with the Office of the President of Georgia Institute of Technology Contact: mark.smith@carnegie.gatech.edu Jerome M Shapiro is with Aware, Inc of Bedford, MA shapiro@aware.com William A Pearlman is with Center for Image Processing Research in the Electri- cal and Computer Engineering Department of Rensselaer Polytechnique Institute, Troy, NY; Amir Said is with Iterated Systems of Atlanta, GA Contact: pearlman@ecse.rpi.edu Zixiang Xiong, Kannan Ramchandran, and Michael T Orchard are with the Departments of Electrical Engineering of the University of Hawaii, Honolulu, HI, the University of Illinois, Urbana, IL, and Princeton University, Princeton, NJ, respectively zx@lena.eng.hawaii.edu; kannan@ifp.uiuc.edu; orchard@ee.princeton.edu Rajan Joshi is with the Imaging Science Division of Eastman Kodak Company, Rochester, NY, and Thomas R Fischer is with the School of Electrical Engineering and Computer Science at Washington State University in Pullman, WA rjoshi@kodak.com; fischer@eecs.wsu.edu John D Villasenor and Jiangtao Wen are with the Integrated Circuits and Systems Laboratory of the University of California, Los Angeles, CA villa@icsl.ucla.edu; gwen@icsl.ucla.edu Geoffrey Davis is with the Mathematics Department of Dartmouth College, Hannover, NH davis@cs.dartmouth.edu Jun Tian and Raymond O Wells, Jr are with the Computational Mathematics Laboratory of Rice University, Houston, TX juntian@math.rice.edu; wells@rice.edu Trac D Tran and Truong Q Nguyen are with the Departments of Electrical and Computer Engineering at the Univeristy of Wisconsin, Madison, WI, and Boston University, Boston, MA, respectively, tran@saigon.ece.wisc.edu; nguyent@bu.edu K Metin Uz and Didier J LeGall are with C-Cube Microsystems of Milpitas, CA, and Martin Vetterli is with Communication Systems Division of the Ecole 436 Polytechnique Federale de Lausanne, Lausanne, Switzerland, and the Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA metin@c-cube.com; didier@c-cube.com; martin.vetterli@de.epfl.ch, martin@eecs.berkeley.edu Wilson C Chung, Faouzi Kossentini are with the School of Engineering, and Mark J T Smith is with the Office of the President of Georgia Institute of Technology Contact: mark.smith@carnegie.gatech.edu Ralph Neff and Avideh Zakhor are with the Department of Electrical Engineering and Computer Science at the University of California, Berkeley, CA falcon@eecs.berkeley.edu; avz@eecs.berkeley.edu Soo-Chul Han and John W Woods are with the Center for Image Processing Research in the ECSE Department of Rennselaer Polytechnique Institute, Troy, NY sooch@ipl.rpi.edu; woods@ecse.rpi.edu William A Pearlman, Beong-Jo Kim, and Zixiang Xiong were at the Center for Image Processing Research in the ECSE Department of Rensselaer Polytechnique Institute, Troy, NY Xiong is now at the University of Hawaii Contact: pearlman@eecs.rpi.edu Index aliasing, 27 fast (FFT), 23 analysis filters, 52 arithmetic coding, 66 Short-Time (STFT), 42 fractals, 239-251 bases, orthogonal, 16,20,38 biorthogonal, 17,20 bit allocation, 73,99,175,201 block transforms, 73-75,303-314 frames, 30 frequency bands, 25-26 frequency localization, 38 Gabor wavelets, 43,366 Gaussians, 36-37 Givens, 33 Cauchy-Schwartz, 19 classification, 199-203 coding, see compression complexity, 95,112,116,221,342,373 compression, image, parts II,III lossless, 3,63 H.263, 321,355,364,375-380 Haar, filter, 47 wavelet, 47-48 Heisenberg Inequality, 37 lossy, 3,73 highpass filter, 26 Hilbert space, 20 video, part IV histogram, 6-7,28 Huffman coding, 64 correlation, 24, 101 human visual system (HVS), 79,103-107 Daubechies filters, 56 delta function, 21 discrete cosine transform (DCT), 74 distortion measures, 71,78 downsampling, 53 image compression, block transform, 73-75,303-314 embedded, 124 JPEG, 73-78 VQ, 73 energy compaction, 18,30 inner product, 16,19 Discrete Fourier Transform (DFT), wavelet, 76 entropy coding, 63,222-233 EZW algorithm, 123 JPEG, 2,5,73-78 filter banks, Karhunen-Loeve Transform (KLT), 74,264 alias-cancelling (AC), 54 finite impulse response (FIR), 24,51 perfect reconstruction (PR), 54 quadrature mirror (QM), 55 two-channel, 51 filters, bandpass, 25 Daubechies, 26 Haar, 26 highpass, 26 lowpass, 25 multiplication-free, 116 fingerprint compression, 271-287 Fourier Transform (FT), continuous, 21,38 discrete, 22 lowpass filter, 25 matching pursuit, 362 matrices, 17 mean, 29 mean-squared error (MSE), 71 motion-compensation, 333,364,375,385,411 MPEG, 3,319-322,361 multiresolution analysis, 45 Nyquist rate, 23,25 orthogonal, basis, 16,20 438 transform, 20 perfect reconstruction, 54-55 wavelet transform (WT), continuous, 43 discrete, 45,76 probability, 28-30 distribution, 29,77 Wigner Distribution, 41 pyramids, 75-76,328-337 zerotrees, 130,163,173,249,404 z-Transform, 25 quantization, error, 68 Lloyd-Max, 69-70 scalar, 68,175 trellis-coded (TCQ), 206 vector, 70 resolution, 45 run-length coding, 66,222-233 sampling theorem, 23,38 spectrogram, 42 SPIHT algorithm, 157 standard deviation, 29 subband coding, 96 symmetry, 25,84 synthesis, 52 time-frequency, 40 transform, discrete cosine, 74 Fourier, 21 Gabor, 43 orthogonal, 16 unitary, 16,34 wavelet, 43 trees, binary, 57,65 hierarchical, 162,173,1 significance, 130,162,177 upsampling, 53 vector spaces, 15,19 video compression, object-based, 383-395 motion-compensated, 333,364,375,385,411 standards, 4,319-322,361 wavelet-based,349.364.379,385,399 wavelet packets 57,187,196-197 ... gains A key objective of MPEG-4 is to achieve object-level access in the video stream, and chapter 23 (“Object-Based Subband /Wavelet Video Compression? ??) by Soo-Chul Han and John Woods directly attempts... Kossentini and Mark Smith, adapts the motion-compensation and I-frame/P-frame structure of MPEG-2, but introduces spatio-temporal subband decompositions instead of DCTs Within the spatio-temporal subbands,... Chapter 15 (? ?Wavelet- Based Embedded Multispectral Image Compression? ??) by Pankaj Topiwala develops an embedded coder in the con- text of a multiband image format This is an extension of standard color