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# Arithmetic coding

About: Arithmetic coding is a research topic. Over the lifetime, 3019 publications have been published within this topic receiving 67128 citations.

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01 Jan 1991TL;DR: The author explains the design and implementation of the Levinson-Durbin Algorithm, which automates the very labor-intensive and therefore time-heavy and expensive process of designing and implementing a Quantizer.

Abstract: 1 Introduction- 11 Signals, Coding, and Compression- 12 Optimality- 13 How to Use this Book- 14 Related Reading- I Basic Tools- 2 Random Processes and Linear Systems- 21 Introduction- 22 Probability- 23 Random Variables and Vectors- 24 Random Processes- 25 Expectation- 26 Linear Systems- 27 Stationary and Ergodic Properties- 28 Useful Processes- 29 Problems- 3 Sampling- 31 Introduction- 32 Periodic Sampling- 33 Noise in Sampling- 34 Practical Sampling Schemes- 35 Sampling Jitter- 36 Multidimensional Sampling- 37 Problems- 4 Linear Prediction- 41 Introduction- 42 Elementary Estimation Theory- 43 Finite-Memory Linear Prediction- 44 Forward and Backward Prediction- 45 The Levinson-Durbin Algorithm- 46 Linear Predictor Design from Empirical Data- 47 Minimum Delay Property- 48 Predictability and Determinism- 49 Infinite Memory Linear Prediction- 410 Simulation of Random Processes- 411 Problems- II Scalar Coding- 5 Scalar Quantization I- 51 Introduction- 52 Structure of a Quantizer- 53 Measuring Quantizer Performance- 54 The Uniform Quantizer- 55 Nonuniform Quantization and Companding- 56 High Resolution: General Case- 57 Problems- 6 Scalar Quantization II- 61 Introduction- 62 Conditions for Optimality- 63 High Resolution Optimal Companding- 64 Quantizer Design Algorithms- 65 Implementation- 66 Problems- 7 Predictive Quantization- 71 Introduction- 72 Difference Quantization- 73 Closed-Loop Predictive Quantization- 74 Delta Modulation- 75 Problems- 8 Bit Allocation and Transform Coding- 81 Introduction- 82 The Problem of Bit Allocation- 83 Optimal Bit Allocation Results- 84 Integer Constrained Allocation Techniques- 85 Transform Coding- 86 Karhunen-Loeve Transform- 87 Performance Gain of Transform Coding- 88 Other Transforms- 89 Sub-band Coding- 810 Problems- 9 Entropy Coding- 91 Introduction- 92 Variable-Length Scalar Noiseless Coding- 93 Prefix Codes- 94 Huffman Coding- 95 Vector Entropy Coding- 96 Arithmetic Coding- 97 Universal and Adaptive Entropy Coding- 98 Ziv-Lempel Coding- 99 Quantization and Entropy Coding- 910 Problems- III Vector Coding- 10 Vector Quantization I- 101 Introduction- 102 Structural Properties and Characterization- 103 Measuring Vector Quantizer Performance- 104 Nearest Neighbor Quantizers- 105 Lattice Vector Quantizers- 106 High Resolution Distortion Approximations- 107 Problems- 11 Vector Quantization II- 111 Introduction- 112 Optimality Conditions for VQ- 113 Vector Quantizer Design- 114 Design Examples- 115 Problems- 12 Constrained Vector Quantization- 121 Introduction- 122 Complexity and Storage Limitations- 123 Structurally Constrained VQ- 124 Tree-Structured VQ- 125 Classified VQ- 126 Transform VQ- 127 Product Code Techniques- 128 Partitioned VQ- 129 Mean-Removed VQ- 1210 Shape-Gain VQ- 1211 Multistage VQ- 1212 Constrained Storage VQ- 1213 Hierarchical and Multiresolution VQ- 1214 Nonlinear Interpolative VQ- 1215 Lattice Codebook VQ- 1216 Fast Nearest Neighbor Encoding- 1217 Problems- 13 Predictive Vector Quantization- 131 Introduction- 132 Predictive Vector Quantization- 133 Vector Linear Prediction- 134 Predictor Design from Empirical Data- 135 Nonlinear Vector Prediction- 136 Design Examples- 137 Problems- 14 Finite-State Vector Quantization- 141 Recursive Vector Quantizers- 142 Finite-State Vector Quantizers- 143 Labeled-States and Labeled-Transitions- 144 Encoder/Decoder Design- 145 Next-State Function Design- 146 Design Examples- 147 Problems- 15 Tree and Trellis Encoding- 151 Delayed Decision Encoder- 152 Tree and Trellis Coding- 153 Decoder Design- 154 Predictive Trellis Encoders- 155 Other Design Techniques- 156 Problems- 16 Adaptive Vector Quantization- 161 Introduction- 162 Mean Adaptation- 163 Gain-Adaptive Vector Quantization- 164 Switched Codebook Adaptation- 165 Adaptive Bit Allocation- 166 Address VQ- 167 Progressive Code Vector Updating- 168 Adaptive Codebook Generation- 169 Vector Excitation Coding- 1610 Problems- 17 Variable Rate Vector Quantization- 171 Variable Rate Coding- 172 Variable Dimension VQ- 173 Alternative Approaches to Variable Rate VQ- 174 Pruned Tree-Structured VQ- 175 The Generalized BFOS Algorithm- 176 Pruned Tree-Structured VQ- 177 Entropy Coded VQ- 178 Greedy Tree Growing- 179 Design Examples- 1710 Bit Allocation Revisited- 1711 Design Algorithms- 1712 Problems

7,015 citations

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TL;DR: The embedded zerotree wavelet algorithm (EZW) is a simple, yet remarkably effective, image compression algorithm, having the property that the bits in the bit stream are generated in order of importance, yielding a fully embedded code.

Abstract: The embedded zerotree wavelet algorithm (EZW) is a simple, yet remarkably effective, image compression algorithm, having the property that the bits in the bit stream are generated in order of importance, yielding a fully embedded code The embedded code represents a sequence of binary decisions that distinguish an image from the "null" image Using an embedded coding algorithm, an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly Also, given a bit stream, the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream In addition to producing a fully embedded bit stream, the EZW consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images Yet this performance is achieved with a technique that requires absolutely no training, no pre-stored tables or codebooks, and requires no prior knowledge of the image source The EZW algorithm is based on four key concepts: (1) a discrete wavelet transform or hierarchical subband decomposition, (2) prediction of the absence of significant information across scales by exploiting the self-similarity inherent in images, (3) entropy-coded successive-approximation quantization, and (4) universal lossless data compression which is achieved via adaptive arithmetic coding >

5,559 citations

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TL;DR: The state of the art in data compression is arithmetic coding, not the better-known Huffman method, which gives greater compression, is faster for adaptive models, and clearly separates the model from the channel encoding.

Abstract: The state of the art in data compression is arithmetic coding, not the better-known Huffman method. Arithmetic coding gives greater compression, is faster for adaptive models, and clearly separates the model from the channel encoding.

3,188 citations

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31 Dec 1992

TL;DR: This chapter discusses JPEG Syntax and Data Organization, the history of JPEG, and some of the aspects of the Human Visual Systems that make up JPEG.

Abstract: Foreword. Acknowledgments. Trademarks. Introduction. Image Concepts and Vocabulary. Aspects of the Human Visual Systems. The Discrete Cosine Transform (DCT). Image Compression Systems. JPEG Modes of Operation. JPEG Syntax and Data Organization. Entropy Coding Concepts. JPEG Binary Arithmetic Coding. JPEG Coding Models. JPEG Huffman Entropy Coding. Arithmetic Coding Statistical. More on Arithmetic Coding. Probability Estimation. Compression Performance. JPEG Enhancements. JPEG Applications and Vendors. Overview of CCITT, ISO, and IEC. History of JPEG. Other Image Compression Standards. Possible Future JPEG Directions. Appendix A. Appendix B. References. Index.

3,183 citations

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Hewlett-Packard

^{1}TL;DR: LOCO-I as discussed by the authors is a low complexity projection of the universal context modeling paradigm, matching its modeling unit to a simple coding unit, which is based on a simple fixed context model, which approaches the capability of more complex universal techniques for capturing high-order dependencies.

Abstract: LOCO-I (LOw COmplexity LOssless COmpression for Images) is the algorithm at the core of the new ISO/ITU standard for lossless and near-lossless compression of continuous-tone images, JPEG-LS. It is conceived as a "low complexity projection" of the universal context modeling paradigm, matching its modeling unit to a simple coding unit. By combining simplicity with the compression potential of context models, the algorithm "enjoys the best of both worlds." It is based on a simple fixed context model, which approaches the capability of the more complex universal techniques for capturing high-order dependencies. The model is tuned for efficient performance in conjunction with an extended family of Golomb (1966) type codes, which are adaptively chosen, and an embedded alphabet extension for coding of low-entropy image regions. LOCO-I attains compression ratios similar or superior to those obtained with state-of-the-art schemes based on arithmetic coding. Moreover, it is within a few percentage points of the best available compression ratios, at a much lower complexity level. We discuss the principles underlying the design of LOCO-I, and its standardization into JPEC-LS.

1,668 citations