Foundations of quantization for probability distributions

TitleFoundations of quantization for probability distributions
Publication TypeBook
Year of Publication2000
AuthorsSiegfried Graf, and Harald Luschgy
PublisherSpringer-Verlag New York, Inc.
CitySecaucus, NJ, USA
ISBN Number3540673946
Keywordsasymptotics, data compression, fractal geometry, information theory, multidimensional quantization, optimal quantizers, 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 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.