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.
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The term "quantization" in the title originates in the theory of signal processing. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
quantizer problem, ball lower bound, quantization dimension, strong separation condition, finite antichain, min llx, quantizer advantage, admissible lattice, inf nen, distortion dimension, quantization coefficient, open set condition, optimal quantizers, bijective isometries, underlying norm, quantization problem, covering radius, nonempty compact set, similarity dimension, measurable partition, covering problem, quantization error, univariate distributions, rectifiable curve, box dimension Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lemma Let, Proof Let, Proposition Let, Theorem Let, Example Let, Corollary Let, Proof Set, Proof That, Definition Let, Proof Immediate, Proof Obvious New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The term "quantization" in the title originates in the theory of signal processing. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
quantizer problem, ball lower bound, quantization dimension, strong separation condition, finite antichain, min llx, quantizer advantage, admissible lattice, inf nen, distortion dimension, quantization coefficient, open set condition, optimal quantizers, bijective isometries, underlying norm, quantization problem, covering radius, nonempty compact set, similarity dimension, measurable partition, covering problem, quantization error, univariate distributions, rectifiable curve, box dimension Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lemma Let, Proof Let, Proposition Let, Theorem Let, Example Let, Corollary Let, Proof Set, Proof That, Definition Let, Proof Immediate, Proof Obvious New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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- Cluster Analysis for Applications (Probability & Mathematical Statistics Monograph) by Michael R. Anderberg in Back Matter
- Geometry of Numbers, Second Edition (North-Holland Mathematical Library) by C.G. Lekkerkerker in Back Matter
- Analysis of and on Uniformly Rectifiable Sets (Mathematical Surveys and Monographs) by Guy David in Back Matter
- Tilings and Patterns by Branko Grunbaum in Back Matter
- Geometric Measure Theory (Classics in Mathematics) by Herbert Federer in Back Matter
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- Geometric Curve Evolution and Image Processing (Lecture Notes in Mathematics) by Frédéric Cao in Back Matter
- hp-Finite Element Methods for Singular Perturbations (Lecture Notes in Mathematics) by Jens M. Melenk in Back Matter
- Big Queues (Lecture Notes in Mathematics) by Ayalvadi J. Ganesh in Back Matter
- Geometric Aspects of Functional Analysis: Israel Seminar 2001-2002 (Lecture Notes in Mathematics) by Vitali D. Milman in Back Matter
- The Valuative Tree (Lecture Notes in Mathematics) by Charles Favre in Back Matter
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