Introduction to Wavelets and Some Applications

Table of Contents

• Title Page
• Fourier Analysis
  • Fourier Series
  • Application of Transforms
  • Representation
  • Example of Slow Convergence
  • Desire for Localization
• The Haar Transform
  • Basic Haar and Wavelet Transform
  • Orthogonal Projections
  • Recursive Property
  • Filter Bank
  • Fast Transform
  • Wavelet Template
  • 2-D Tensor Product Haar
• Overview of Tree Approximation and Encoding
  • Tree Encoding
  • Network Application
  • Client/Server Model
  • Features of Tree-Encoded Bitstream
• Algorithm for Tree Approximation and Encoding
  • Thresholding
  • Spanning Trees
  • Bitplanes and Tree Growth
  • Dyadic Represention for Upper Half Plane
  • Bitstream Formation
• Burn-In: Implementation of Algorithm
  • Client Windows Interface
  • Region Selection - Pruning
  • Offset Markers into Bitstream
  • Progressive Burn-In #1
  • Progressive Burn-In #2
  • Progressive Burn-In #3
  • Progressive Burn-In #4
  • Features of Encoder
• End

Email: sharpley@math.sc.edu

Home Page: http://www.math.sc.edu/~sharpley