Foundations of Quantization for Probability Distributions

1. Front Matter

   Pages i-x

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2. Introduction

   • Siegfried Graf, Harald Luschgy

   Pages 1-5

3. General properties of the quantization for probability distributions

   • Siegfried Graf, Harald Luschgy

   Pages 7-75

4. Asymptotic quantization for nonsingular probability distributions

   • Siegfried Graf, Harald Luschgy

   Pages 77-154

5. Asymptotic quantization for singular probability distributions

   • Siegfried Graf, Harald Luschgy

   Pages 155-207

6. Back Matter

   Pages 209-230

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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.

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

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