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Mathematics - Probability Theory and Stochastic Processes | Foundations of Quantization for Probability Distributions

Foundations of Quantization for Probability Distributions

Series: Lecture Notes in Mathematics, Vol. 1730

Graf, Siegfried, Luschgy, Harald

2000, X, 230 p.

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  • About this book

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.

Content Level » Research

Keywords » Cluster analysis - Measure - Pattern Recognition - Probability distribution - Probability theory - data compression - image processing - information - information theory - operations research - sets

Related subjects » Image Processing - Operations Research & Decision Theory - Probability Theory and Stochastic Processes - Signals & Communication - Statistical Theory and Methods

Table of contents 

General properties of the quantization for probability distributions.- Asymptotic quantization for nonsingular probability distributions.- Asymptotic quantization for singular probability distributions.

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