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Foundations of Quantization for Probability Distributions

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...

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Bibliographic Details
Main Authors: Graf, Siegfried, Luschgy, Harald (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2000, 2000
Edition:1st ed. 2000
Series:Lecture Notes in Mathematics
Subjects:
Statistical Theory And Methods
Operations Research
Statistics 
Probability Theory
Telecommunication
Communications Engineering, Networks
Automated Pattern Recognition
Operations Research And Decision Theory
Probabilities
Pattern Recognition Systems
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I. General properties of the quantization for probability distributions: Voronoi partitions. Centers and moments of probability distributions. The quantization problem. Basic properties of optimal quantizers. Uniqueness and optimality in one dimension
  • II. Asymptotic quantization for nonsingular probability distributions: Asymptotics for the quantization error. Asymptotically optimal quantizers. Regular quantizers and quantization coefficients. Random quantizers and quantization coefficients. Asymptotics for the covering radius
  • III. Asymptotic quantization for singular probability distributions: The quantization dimension. Regular sets and measures of dimension D. Rectifiable curves. Self-similar sets and measures

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