LEADER 05520nam 2200709Ia 450 001 9910139468203321 005 20210209181001.0 010 $a1-282-16536-4 010 $a9786612165368 010 $a0-470-61156-1 010 $a0-470-39422-6 035 $a(CKB)2550000000005842 035 $a(EBL)477630 035 $a(OCoLC)520990463 035 $a(SSID)ssj0000342644 035 $a(PQKBManifestationID)11243663 035 $a(PQKBTitleCode)TC0000342644 035 $a(PQKBWorkID)10284708 035 $a(PQKB)10472990 035 $a(MiAaPQ)EBC477630 035 $a(MiAaPQ)EBC4036964 035 $a(PPN)190071206 035 $a(EXLCZ)992550000000005842 100 $a20070615d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aScaling, fractals and wavelets$b[electronic resource] /$fedited by Patrice Abry, Paulo Gonc?alves, Jacques Levy Vehel 210 $aLondon $cISTE ;$aHoboken, NJ $cWiley$d2009 215 $a1 online resource (506 p.) 225 1 $aISTE ;$vv.74 300 $aDescription based upon print version of record. 311 $a1-84821-072-8 320 $aIncludes bibliographical references. 327 $aScaling, Fractals and Wavelets; Table of Contents; Preface; Chapter 1. Fractal and Multifractal Analysis in Signal Processing; 1.1. Introduction; 1.2. Dimensions of sets; 1.2.1. Minkowski-Bouligand dimension; 1.2.2. Packing dimension; 1.2.3. Covering dimension; 1.2.4. Methods for calculating dimensions; 1.3. Ho?lder exponents; 1.3.1. Ho?lder exponents related to a measure; 1.3.2. Theorems on set dimensions; 1.3.3. Ho?lder exponent related to a function; 1.3.4. Signal dimension theorem; 1.3.5. 2-microlocal analysis; 1.3.6. An example: analysis of stock market price; 1.4. Multifractal analysis 327 $a1.4.1. What is the purpose of multifractal analysis?1.4.2. First ingredient: local regularity measures; 1.4.3. Second ingredient: the size of point sets of the same regularity; 1.4.4. Practical calculation of spectra; 1.4.5. Refinements: analysis of the sequence of capacities, mutual analysis and multisingularity; 1.4.6. The multifractal spectra of certain simple signals; 1.4.7. Two applications; 1.4.7.1. Image segmentation; 1.4.7.2. Analysis of TCP traffic; 1.5. Bibliography; Chapter 2. Scale Invariance and Wavelets; 2.1. Introduction; 2.2. Models for scale invariance; 2.2.1. Intuition 327 $a2.2.2. Self-similarity2.2.3. Long-range dependence; 2.2.4. Local regularity; 2.2.5. Fractional Brownian motion: paradigm of scale invariance; 2.2.6. Beyond the paradigm of scale invariance; 2.3.Wavelet transform; 2.3.1. Continuous wavelet transform; 2.3.2. Discretewavelet transform; 2.4. Wavelet analysis of scale invariant processes; 2.4.1. Self-similarity; 2.4.2. Long-range dependence; 2.4.3. Local regularity; 2.4.4. Beyond second order; 2.5. Implementation: analysis, detection and estimation; 2.5.1. Estimation of the parameters of scale invariance 327 $a2.5.2. Emphasis on scaling laws and determination of the scaling range2.5.3. Robustness of the wavelet approach; 2.6. Conclusion; 2.7. Bibliography; Chapter 3. Wavelet Methods for Multifractal Analysis of Functions; 3.1. Introduction; 3.2. General points regarding multifractal functions; 3.2.1. Important definitions; 3.2.2. Wavelets and pointwise regularity; 3.2.3. Local oscillations; 3.2.4. Complements; 3.3. Random multifractal processes; 3.3.1. Le?vy processes; 3.3.2. Burgers' equation and Brownian motion; 3.3.3. Random wavelet series; 3.4. Multifractal formalisms 327 $a3.4.1. Besov spaces and lacunarity3.4.2. Construction of formalisms; 3.5. Bounds of the spectrum; 3.5.1. Bounds according to the Besov domain; 3.5.2. Bounds deduced from histograms; 3.6. The grand-canonical multifractal formalism; 3.7. Bibliography; Chapter 4. Multifractal Scaling: General Theory and Approach by Wavelets; 4.1. Introduction and summary; 4.2. Singularity exponents; 4.2.1. Ho?lder continuity; 4.2.2. Scaling of wavelet coefficients; 4.2.3. Other scaling exponents; 4.3. Multifractal analysis; 4.3.1. Dimension based spectra; 4.3.2. Grain based spectra 327 $a4.3.3. Partition function and Legendre spectrum 330 $aScaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling ? self-similarity, long-range dependence and multi-fractals ? are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed 410 0$aISTE 606 $aSignal processing$xMathematics 606 $aFractals 606 $aWavelets (Mathematics) 615 0$aSignal processing$xMathematics. 615 0$aFractals. 615 0$aWavelets (Mathematics) 676 $a621.382/20151 676 $a621.38220151 701 $aAbry$b Patrice$0951598 701 $aGonc?alves$b Paulo$f1967-$0951599 701 $aLe?vy Ve?hel$b Jacques$f1960-$0951600 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139468203321 996 $aScaling, fractals and wavelets$92151316 997 $aUNINA