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

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Foundations of Quantization for Probability Distributions

By: Siegfried Graf, Harald Luschgy

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Hardcover | 1 June 2000

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244 Pages

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23.39 x 15.6 x 1.42

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Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and 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 and special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers and graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above.

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List of Figures
List of Tables
Introduction	p. 1
General properties of the quantization for probability distributions	p. 7
Voronoi partitions	p. 7
Centers and moments of probability distributions	p. 20
The quantization problem	p. 30
Basic Properties of optimal quantizers	p. 37
Uniqueness and optimality in one dimension	p. 64
Asymptotic quantization for nonsingular probability distributions	p. 77
Asymptotics for the quantization error	p. 77
Asymptotically optimal quantizes	p. 93
Regular quantizers and quantization coefficients	p. 106
Random quantizers and quantization coefficients	p. 127
Asymptotics for the covering radius	p. 137
Asymptotic quantization for singular probability distributions	p. 155
The quantization dimension	p. 155
Regular sets and measures of dimension D	p. 165
Rectifiable curves	p. 180
Self-similar sets and measures	p. 190
Appendix: Univariate distributions	p. 209
Bibliography	p. 215
Symbols	p. 225
Index	p. 229
Table of Contents provided by Blackwell. All Rights Reserved.

Foundations of Quantization for Probability Distributions

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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