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Foundations of Quantization for Probability Distributions : Lecture Notes in Mathematics - Siegfried Graf

Foundations of Quantization for Probability Distributions

Lecture Notes in Mathematics

Paperback Published: June 2000
ISBN: 9783540673941
Number Of Pages: 230

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Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal & image processing & information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, & operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous & special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers & graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above.

List of Figures
List of Tables
Introductionp. 1
General properties of the quantization for probability distributionsp. 7
Voronoi partitionsp. 7
Centers and moments of probability distributionsp. 20
The quantization problemp. 30
Basic Properties of optimal quantizersp. 37
Uniqueness and optimality in one dimensionp. 64
Asymptotic quantization for nonsingular probability distributionsp. 77
Asymptotics for the quantization errorp. 77
Asymptotically optimal quantizesp. 93
Regular quantizers and quantization coefficientsp. 106
Random quantizers and quantization coefficientsp. 127
Asymptotics for the covering radiusp. 137
Asymptotic quantization for singular probability distributionsp. 155
The quantization dimensionp. 155
Regular sets and measures of dimension Dp. 165
Rectifiable curvesp. 180
Self-similar sets and measuresp. 190
Appendix: Univariate distributionsp. 209
Bibliographyp. 215
Symbolsp. 225
Indexp. 229
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540673941
ISBN-10: 3540673946
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 230
Published: June 2000
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.42
Weight (kg): 0.52

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