| 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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