Wavelet Analysis and Its Applications.

Abstract

Time-frequency localization is one of the most essential features of the wavelet transform. It was shown that while high order Daubechies and Battle-Lemarie wavelets give poor time-frequency localizations, the Chui-Wang spline-wavelets provide asymptotically optimal time- frequency windows. On the other hand, we also showed that by using the scale 3 instead of 2, symmetry can be achieved by orthonormal wavelets with compact support. Multivariate wavelets, particularly those with matrix dilation, were studied, and the theory of oversampling frames was extended to this setting. Interpolating wavelets have distributional duals that lead to the notion of functional wavelet transform. Other extensions required a study of the stability issue and algorithmic construction in multivariate splines. Applications to systems theory lead to the study of Hankel approximation and localization of neural networks.

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Document Details

Document Type
Technical Report
Publication Date
Jan 24, 1995
Accession Number
ADA301762

Entities

People

  • Charles K. Chui

Organizations

  • Texas A&M University

Tags

Communities of Interest

  • Air Platforms
  • Space

DTIC Thesaurus Topics

  • Algorithms
  • Construction
  • Engineering
  • Frequency
  • Information Operations
  • Integrals
  • Linear Systems
  • Mathematics
  • Military Research
  • Neural Networks
  • Personnel Management
  • Scientists
  • Symmetry
  • Systems Analysis
  • Triangulation
  • Universities
  • Wavelet Transforms

Readers

  • Approximation Theory.
  • Image Processing and Computer Vision.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms