The comprehensive compendium furnishes a quick and efficient entry point to many multiresolution techniques and facilitates the transition from an idea into a real project. It focuses on methods combining several soft computing techniques (fuzzy logic, neural networks, genetic algorithms) in a multiresolution framework.

Illustrated with numerous vivid examples, this useful volume gives the reader the necessary theoretical background to decide which methods suit his/her needs.

New materials and applications for multiresolution analysis are added, including notable research topics such as deep learning, graphs, and network analysis.

Contents:

• 
  

  Foreword

  
  


• 
  

  Introduction to the Second Edition

  
  


• 
  

  Introduction to Wavelet Theory:

  
  
  
  
  • A Short Overview of the Development of Wavelet Theory
  
  
  • Wavelet Transform versus Fourier Transform
  
  
  • The Fast Wavelet Transform
  
  
  • Definition of a Multiresolution
  
  
  • Biorthogonal Wavelets
  
  
  • Wavelets and Subband Coding
  
  
  • Contourlets and Shearlet
  
  
  • Empirical Wavelet Decomposition
  
  
  • Applications
  
  
  • Recent Applications of Wavelet and Multiresolution Analysis
  
  
  
  


• 
  

  Preprocessing: The Multiresolution Approach:

  
  
  
  
  • The Double Curse: Dimensionality and Complexity
  
  
  • Dimension Reduction
  
  
  • Karhunen-Loève Transform (Principal Components Analysis)
  
  
  • Dimension Reduction Through Wavelet-Based Projection Methods
  
  
  • Exploratory Knowledge Extraction
  
  
  • Wavelets in Classification
  
  
  • Applications of Multiresolution Techniques for Preprocessing in Soft Computing
  
  
  
  


• 
  

  Spline-Based Wavelets Approximation and Compression Algorithms:

  
  
  
  
  • Spline-Based Wavelets
  
  
  • A Selection of Wavelet-Based Algorithms for Spline Approximation
  
  
  
  


• 
  

  Automatic Generation of a Fuzzy System with Wavelet-Based Methods and Spline-Based Wavelets:

  
  
  
  
  • Fuzzy Rule-Based Systems
  
  
  • Type-2 Fuzzy Systems
  
  
  • Interpolation, Extrapolation, and Approximation Methods
  
  
  • Fuzzy Wavelet
  
  
  • Soft Computing Approach to Fuzzy Wavelet Transform
  
  
  
  


• 
  

  Nonparametric Wavelet-Based Estimation and Regression Techniques:

  
  
  
  
  • Introduction
  
  
  • Smoothing Splines
  
  
  • Wavelet Estimators
  
  
  • Wavelet Methods for Curve Estimation
  
  
  • Fuzzy Wavelet Estimators
  
  
  
  


• 
  

  Hybrid Neural Networks:

  
  
  
  
  • Neuro-Fuzzy Modeling
  
  
  • Wavelet-Based Neural Networks
  
  
  • Extreme Learning Machines
  
  
  • Dyadic Wavelet Networks Or Wavenets
  
  
  • Wavelet-Based Fuzzy Neural Networks
  
  
  • Applications of Wavelet, Fuzzy Wavelet Networks, and Wavenets
  
  
  
  


• 
  

  Multiresolution and Deep Neural Networks:

  
  
  
  
  • Introduction
  
  
  • Convolutional Neural Networks (CNN) and Multiresolution
  
  
  • Generative Adversarial Networks (GAN)
  
  
  • U-Nets and Multiresolution
  
  
  • Fuzzy Logic in Deep Learning
  
  
  
  


• 
  

  Developing Intelligent Sensors with Fuzzy Logic and Multiresolution Analysis:

  
  
  
  
  • Application of Multiresolution and Fuzzy Logic to Fire Detection
  
  
  • Transparency
  
  
  • Man, Sensors, and Computer Intelligence
  
  
  • Constructive Modeling
  
  
  • From a Sensor to a Smart Sensor Network with Multicriteria Decisions
  
  
  
  


• 
  

  Multiresolution and Wavelets in Graphs, Trees, and Networks:

  
  
  
  
  • Wavelet Decomposition on a Graph
  
  
  • Treelet
  
  
  • Phylogenetic Trees and Networks
  
  
  • Multiresolution Approach to Phylogeny
  
  
  • Applications to Phylogeography
  
  
  • Continuous Characters: Classification of Galaxies
  
  
  • Outlook
  
  
  
  


• 
  

  Genetic Algorithms and Multiresolution:

  
  
  
  
  • The Standard Genetic Algorithm
  
  
  • Walsh Functions and Genetic Algorithms
  
  
  • Wavelet-Based Genetic Algorithms
  
  
  • Population Evolution and Deceptive Functions
  
  
  • Multiresolution Search
  
  
  • Searching for a Good Solution: How to Beat Brute Force
  
  
  • Swarm Intelligence
  
  
  
  


• 
  

  Annexes:

  
  
  
  
  • Annex A: Lifting Scheme
  
  
  • Introduction
  
  
  • Biorthogonal Spline-Wavelets Constructions with the Lifting Scheme
  
  
  • Annex B: Nonlinear Wavelets
  
  
  • Said and Pearlman Wavelets
  
  
  • Morphological Haar Wavelets
  
  
  • Annex C: Phylogenetic Trees and Networks (Outerplanar Networks)
  
  
  
  


• 
  

  Index

  
  

Readership: Researchers, professionals, academics and graduate students in fuzzy logic.