The theory of quantization began in 1898 with Sheppard's study of roundoff error, but its importance for modulation and analog-to-digital conversion was first recognized during the early development of pulse code modulation systems, especially in the 1948 paper of Oliver, Pierce, and Shannon. Also in 1948, Bennett published the first high resolution analysis of quantization and an exact analysis of quantization noise for Gaussian processes, and Shannon published the beginnings of rate-distortion theory, which would provide a theory for quantization as analog-to-digital conversion and as data compression. Beginning with these three papers of fifty years ago, we trace the history of quantization from its origins through this decade, and we survey the fundamentals of the theory and many of the popular and promising techniques for quantization.
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4923
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Elements of Information Theory
– Cover, Thomas
- 1991
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2573
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Classification and Regression Trees
– Breiman, Friedman, et al.
- 1984
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1125
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Vector Quantization and Signal Compression
– Gersho, Gray
- 1992
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943
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Embedded image coding using zerotrees of wavelet coefficients
– SHAPIRO
- 1993
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846
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Information Theory and Reliable Communication
– Gallager
- 1968
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845
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Some Methods for Classification and Analysis of Multivariate Observations
– MacQueen
- 1967
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844
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An algorithm for vector quantization design
– Linde, Buzo, et al.
- 1980
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793
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Clustering Algorithms
– Hartigan
- 1975
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737
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Multidimensional binary search trees used associative searching
– Bentley
- 1975
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707
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The Laplacian pyramid as a compact image code
– BURT, ADELSON
- 1983
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619
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A Probabilistic Theory of Pattern Recognition
– Devroye, Gyorfi, et al.
- 1996
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613
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A method for the construction of minimum-redundancy codes
– Huffman
- 1952
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553
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Binary codes capable of correcting deletions, insertions and reversals
– Levenshtein
- 1966
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519
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Image Coding Using Wavelet Transform
– Antonini, Barlaud, et al.
- 1992
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501
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The viterbi algorithm
– Forney
- 1973
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420
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Information Theory - Coding Theorems for Discrete Memoryless Systems
– Csiszar, Korner
- 1981
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410
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Cluster Analysis for Applications
– Anderberg
- 1973
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367
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Entropy-based algorithms for best basis selection
– Coifman, Wickerhauser
- 1992
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335
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Wavelets and Subband Coding
– Vetterli, Kovačević
- 1995
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252
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efficient image codec based on set partitioning in hierarchical trees
– Said, Pearlman, et al.
- 1996
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232
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Channel coding with multilevel/phase signals
– Ungerboeck
- 1982
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227
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Efficient bit allocation for an arbitrary set of quantizers
– Shoham, Gersho
- 1988
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220
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Image compression through wavelet transform coding, preprint
– DeVore, Jawerth, et al.
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214
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Self-organization and associative
– Kohonen
- 1989
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206
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Hierarchical grouping to optimize an objective function
– Ward
- 1963
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196
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A mathematical theory of communication,” Bell Syst
– Shannon
- 1948
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177
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Introduction to Data Compression
– Sayood
- 2000
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175
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Design of multiple description scalar quantizers
– Vaishampayan
- 1993
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159
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Best wavelet packet bases in a rate-distortion sense
– Ramchandran, Vetterli
- 1993
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155
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Digital coding of waveforms: principles and applications to speech and video
– Jayant, Noll
- 1984
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154
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Discrete cosine transform
– Ahmed, Natarajan, et al.
- 1974
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145
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Quantizing for minimum distortion
– Max
- 1960
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134
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Subband coding of images
– Woods, O’Neil
- 1986
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132
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Entropy-constrained vector quantization
– Chou, Lookabaugh, et al.
- 1989
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125
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Achievable rates for multiple descriptions
– Gamal, Cover
- 1982
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109
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Image compression using the 2-D wavelet transform
– Lewis, Knowles
- 1992
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100
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Successive refinement of information
– Equitz, Cover
- 1991
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93
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Computation of channel capacity and rate-distortion functions
– Blahut
- 1972
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93
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A study of vector quantization for noisy channels
– Farvardin
- 1990
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93
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Vector quantization in speech coding
– Makhoul, Roucos
- 1985
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85
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Discrete Cosine Transform
– Rao, Yip
- 1990
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83
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Variations on a theme by Huffman
– Gallager
- 1978
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79
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Minimum Prediction Residual Principle Applied to Speech Recognition
– Itakura
- 1975
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77
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Asymptotically efficient quantizing
– Gish, Pierce
- 1968
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74
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Transform Coding of Images
– Clarke
- 1985
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73
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Trellis coded quantization of memoryless and gauss-markov sources
– Marcellin, Fischer
- 1990
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71
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Functional Analysis
– Reed, Simon
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71
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A new vector quantization clustering algorithm
– Equitz
- 1989
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67
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Image Quality Measures and their Performance
– Eskicioglu, Fisher
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66
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Transform coding of audio signals using perceptual noise criteria
– Johnston
- 1988
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