With clear and easy-to-understand explanations, this book covers the fundamental concepts and coding methods of signal compression, whilst still retaining technical depth and rigor. It contains a wealth of illustrations, step-by-step descriptions of algorithms, examples and practice problems, which make it an ideal textbook for senior undergraduate and graduate students, as well as a useful self-study tool for researchers and professionals. Principles of lossless compression are covered, as are various entropy coding techniques, including Huffman coding, arithmetic coding and Lempel-Ziv coding. Scalar and vector quantization and trellis coding are thoroughly explained, and a full chapter is devoted to mathematical transformations including the KLT, DCT and wavelet transforms. The workings of transform and subband/wavelet coding systems, including JPEG2000 and SBHP image compression and H.264/AVC video compression, are explained and a unique chapter is provided on set partition coding, shedding new light on SPIHT, SPECK, EZW and related methods.

William A. Pearlman is a Professor Emeritus in the Electrical, Computer, and Systems Engineering Department at the Rensselear Polytechnic Institute (RPI), where he has been a faculty member since 1979. He has more than 35 years of experience in teaching and researching in the fields of information theory, data compression, digital signal processing, and digital communications theory, and he has written about 250 published works on these fields. He is a Fellow of the IEEE and the SPIE, and he is the co-inventor of two celebrated image compression algorithms: SPIHT and SPECK. Amir Said is currently a Master Researcher at Hewlett-Packard Laboratories, where he has worked since 1998. His research interests include multimedia communications, coding and information theory, image and video compression, signal processing, and optimization, and he has more than 100 publications and 20 patents in these fields. He is co-inventor, also with Dr. Pearlman of the SPIHT image compression algorithm, and co-recipient, also with Dr. Pearlman, of two Best Paper Awards, one from the IEEE Circuits and Systems Society and the other from the IEEE Signal Processing Society.

Preface	p. xv
Acknowledgments	p. xix
Motivation	p. 1
The importance of compression	p. 1
Data types	p. 2
Symbolic information	p. 2
Numerical information	p. 3
Basic compression process	p. 4
Compression applications	p. 5
Design of compression methods	p. 6
Multi-disciplinary aspect	p. 8
Note	p. 8
References	p. 9
Book overview	p. 10
Entropy and lossless coding	p. 10
Quantization	p. 11
Source transformations	p. 12
Prediction	p. 12
Transforms	p. 13
Set partition coding	p. 16
Coding systems	p. 17
Performance criteria	p. 17
Transform coding systems	p. 18
Subband coding systems	p. 19
Distributed source coding	p. 20
Notes	p. 21
References	p. 22
Principles of lossless compression	p. 23
Introduction	p. 23
Lossless source coding and entropy	p. 23
Variable length codes	p. 28
Unique decidability and prefix-free codes	p. 28
Construction of prefix-free codes	p. 28
Kraft inequality	p. 30
Optimality of prefix-free codes	p. 32
Sources with memory	p. 36
Concluding remarks	p. 37
Problems	p. 37
References	p. 40
Entropy coding techniques	p. 41
Introduction	p. 41
Huffman codes	p. 41
Shannon-Fano-Elias codes	p. 47
SFE code examples	p. 48
Decoding the SFE code	p. 49
Arithmetic code	p. 50
Preliminaries	p. 50
Arithmetic encoding	p. 51
Arithmetic decoding	p. 53
Run-length codes	p. 55
Alphabet partitioning: modified Huffman codes	p. 57
Modified Huffman codes	p. 57
Alphabet partitioning	p. 58
Golomb code	p. 60
Dictionary coding	p. 53
The LZ78 code	p. 64
The LZW algorithm	p. 65
The LZ77 coding method	p. 67
Summary remarks	p. 72
Problems	p. 72
Notes	p. 75
References	p. 76
Lossy compression of scalar sources	p. 77
Introduction	p. 77
Quantization	p. 77
Scalar quantization	p. 77
Uniform quantization	p. 81
Non-uniform quantization	p. 87
High rate approximations	p. 89
Companding	p. 91
Distortion at high rates	p. 93
Entropy coding of quantizer outputs	p. 95
Entropy coded quantizer characteristics	p. 98
Null-zone quantization	p. 99
Bounds on optimal performance	p. 101
Rate-distortion theory	p. 102
The Gish-Pierce bound	p. 104
Concluding remarks	p. 107
Appendix: quantization tables	p. 107
Problems	p. 109
Note	p. 113
References	p. 114
Coding of sources with memory	p. 116
Introduction	p. 116
Predictive coding	p. 116
Optimal linear prediction	p. 117
DPCM system description	p. 120
DPCM coding error and gain	p. 121
Vector coding	p. 122
Optimal performance bounds	p. 122
Vector (block) quantization (VQ)	p. 129
Entropy constrained vector quantization	p. 135
Tree-structured vector quantization	p. 141
Variable length TSVQ coding	p. 144
Pruned TSVQ	p. 145
Tree and trellis codes	p. 146
Trellis codes	p. 148
Encoding and decoding of trellis codes	p. 150
Codevector alphabets	p. 152
Trellis coded quantization (TCQ)	p. 152
Entropy-coded TCQ	p. 154
Improving low-rate performance in TCQ	p. 155
Search algorithms	p. 155
M-algorithm	p. 155
The Viterbi algorithm	p. 158
Concluding remarks	p. 160
Problems	p. 160
Notes	p. 163
References	p. 164
Mathematical transformations	p. 166
Introduction	p. 166
Transform coding gain	p. 169
The optimal Karhunen-Loeve transform	p. 171
Optimal transform coding gain	p. 172
Suboptimal transforms	p. 172
The discrete Fourier transform	p. 172
The discrete cosine transform	p. 173
The Hadamard-Walsh transform	p. 174
Lapped orthogonal transform	p. 175
Example of calculation of transform coding gain	p. 178
Transforms via filter banks	p. 179
Two-dimensional transforms for images	p. 181
Subband transforms	p. 184
Introduction	p. 184
Coding gain of subband transformation	p. 187
Realizable perfect reconstruction filters	p. 192
Orthogonal wavelet transform	p. 194
Biorthogonal wavelet transform	p. 199
Useful biorthogonal filters	p. 204
The lifting scheme	p. 205
Transforms with integer output	p. 208
Concluding remarks	p. 211
Problems	p. 212
Notes	p. 214
References	p. 216
Rate control in transform coding systems	p. 218
Rate allocation	p. 218
Optimal rate allocation for known quantizer characteristics	p. 220
Realizing the optimal rate allocation	p. 223
Fixed level quantization	p. 225
Optimal bit allocation for arbitrary set of quantizers	p. 226
Building up to optimal rates for arbitrary quantizers	p. 228
Transform coding gain	p. 230
Subband rate allocation	p. 233
Practical issues	p. 237
Subband coding gain	p. 239
Algorithms for rate allocation to subbands	p. 241
Conclusions	p. 242
Problems	p. 242
Notes	p. 243
References	p. 244
Transform coding systems	p. 245
Introduction	p. 245
Application of source transformations	p. 245
Model-based image transform coding	p. 246
Encoding transform coefficients	p. 249
The JPEG standard	p. 251
The JPEG baseline system	p. 252
Detailed example of JPEG standard method	p. 256
Advanced image transform coding: H.264/AVC intra coding	p. 259
Concluding remarks	p. 262
Problems	p. 262
Notes	p. 263
References	p. 264
Set partition coding	p. 265
Principles	p. 265
Partitioning data according to value	p. 267
Forming partitions recursively: square blocks	p. 270
Binary splitting	p. 274
One-dimensional signals	p. 276
Tree-structured sets	p. 276
A different wavelet transform partition	p. 279
Data-dependent thresholds	p. 282
Adaptive partitions	p. 283
Progressive transmission and bitplane coding	p. 285
Applications to image transform coding	p. 286
Block partition coding and amplitude and group partitioning (AGP)	p. 287
Enhancements via entropy coding	p. 289
Traversing the blocks	p. 289
Embedded block coding of image wavelet transforms	p. 291
A SPECK coding example	p. 291
Embedded tree-based image wavelet transform coding	p. 297
A SPIHT coding example	p. 299
Embedded zerotree wavelet (EZW) coding	p. 302
Group testing for image wavelet coding	p. 306
Conclusion	p. 306
Problems	p. 307
Notes	p. 310
References	p. 311
Subband/wavelet coding systems	p. 313
Wavelet transform coding systems.	p. 313
Generic wavelet-based coding systems	p. 317
Compression methods in wavelet-based systems	p. 318
Block-based wavelet transform set partition coding	p. 320
Progressive resolution coding	p. 321
Quality-progressive coding	p. 323
Octave band partitioning	p. 326
Direct bit-embedded coding methods	p. 328
Lossless coding of quantizer levels with adaptive thresholds	p. 329
Tree-block coding	p. 331
Coding of subband subblocks	p. 332
Coding the initial thresholds	p. 333
The SBHP method	p. 335
JPEG2000 coding	p. 336
The embedded zero-block coder (EZBC)	p. 343
Tree-based wavelet transform coding systems	p. 347
Fully scalable SPIHT	p. 347
Resolution scalable SPIHT	p. 349
Block-oriented SPIHT coding	p. 352
Rate control for embedded block coders	p. 354
Conclusion	p. 356
Notes	p. 357
References	p. 359
Methods for lossless compression of images	p. 361
Introduction	p. 361
Lossless predictive coding	p. 362
Old JPEG standard for lossless image compression	p. 362
State-of-the-art lossless image coding and JPEG-LS	p. 364
The predictor	p. 364
The context	p. 365
Golomb-Rice coding	p. 366
Bias cancellation	p. 366
Run mode	p. 367
Near-lossless mode	p. 368
Remarks	p. 368
Multi-resolution methods	p. 368
Concluding remarks	p. 369
Problems	p. 370
Notes	p. 371
References	p. 372
Color and multi-component image and video coding	p. 373
Introduction	p. 373
Color image representation	p. 374
Chrominance subsampling	p. 376
Principal component space	p. 377
Color image coding	p. 378
Transform coding and JPEG	p. 378
Wavelet transform systems	p. 380
Multi-component image coding	p. 383
JPEG2000	p. 383
Three-dimensional wavelet transform coding	p. 384
Video coding	p. 389
Concluding remarks	p. 395
Notes	p. 395
References	p. 396
Distributed source coding	p. 398
Slepian-Wolf coding for lossless compression	p. 398
Practical Slepian-Wolf coding	p. 400
Wyner-Ziv coding for lossy compression	p. 404
Scalar Wyner-Ziv coding	p. 406
Probability of successful reconstruction	p. 407
Concluding remarks	p. 411
Problems	p. 411
Notes	p. 412
References	p. 413
Index	p. 414
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