Foundations of Quantization for Probability Distributions

• Main Authors: Graf, Siegfried (Author, http://id.loc.gov/vocabulary/relators/aut), Luschgy, Harald (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000.
• Edition: 1st ed. 2000.
• Series: Lecture Notes in Mathematics, 1730
• Subjects: Probabilities.; Statistics .; Pattern recognition.; Operations research.; Decision making.; Electrical engineering.; Probability Theory and Stochastic Processes.; Statistical Theory and Methods.; Pattern Recognition.; Operations Research/Decision Theory.; Communications Engineering, Networks.

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...

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.