Foundations of Quantization for Probability DistributionsDue 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. |
Contents
III | 1 |
IV | 7 |
V | 16 |
VI | 20 |
VIII | 26 |
IX | 30 |
X | 37 |
XII | 48 |
XXXVII | 146 |
XXXVIII | 151 |
XXXIX | 155 |
XL | 165 |
XLII | 173 |
XLIII | 180 |
XLIV | 190 |
XLVI | 192 |
XIII | 50 |
XIV | 52 |
XV | 57 |
XVI | 64 |
XVIII | 66 |
XIX | 77 |
XX | 93 |
XXII | 96 |
XXIII | 99 |
XXIV | 102 |
XXV | 106 |
XXVI | 107 |
XXVIII | 111 |
XXIX | 121 |
XXX | 127 |
XXXII | 130 |
XXXIII | 132 |
XXXIV | 137 |
XXXVI | 141 |
XLVII | 195 |
XLVIII | 199 |
XLIX | 203 |
L | 209 |
LI | 215 |
LII | 225 |
LIII | 229 |
LIV | 1 |
LV | 19 |
LVI | 33 |
LVII | 49 |
LVIII | 61 |
LX | 78 |
LXI | 92 |
LXII | 100 |
LXIII | 114 |
LXIV | 128 |
LXV | 139 |
Other editions - View all
Foundations of Quantization for Probability Distributions Siegfried Graf,Harald Luschgy Limited preview - 2007 |
Foundations of Quantization for Probability Distributions Siegfried Graf,Harald Luschgy No preview available - 2014 |
Foundations of Quantization for Probability Distributions Siegfried Graf,Harald Luschgy No preview available - 2000 |
Common terms and phrases
algorithm analysis applications asymptotically brand called communication consumer context-aware database defined denote DICOM digital divide distance distribution dP(x economy electronic commerce element Emacspeak evaluation evoting Ewha Womans University example exists Figure follows gatekeeper global handoff IEEE industry infrastructure integrated intelligent agents interactive interface Internet knowledge Korea l2-norm lattice learning Lemma live catalog location update Maori mathematics measure method mobile user node objects organization pixel Project-Based Learning Proof proposed PSNR quantization coefficient quantization error query R-tree rectifiable curve result retrieval scheme server sets of centers shows Singapore spherical pyramid SPY-TEC steganography structure supp(P teachers Theorem underlying norm Voronoi diagram Voronoi region voting web-based Zealand αξα