WAVELETS SOFT COMPUTING (2ND ED)

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.