On the Construction of Multivariate (pre) Wavelets

Abstract

A new approach for the construction of wavelets and prewavelets on IR d from multiresolution is presented. The method uses only properties of shift- invariant spaces and orthogonal projectors from L2(IRd) onto these spaces, and requires neither decay nor stability of the scaling function. Furthermore, this approach allows a simple derivation of previous, as well as new, constructions of wavelets, and leads to a complete resolution of questions concerning the nature of the intersection and the union of a scale of spaces to be used in a multiresolution. wavelets, multiresolution, shift-invariant spaces, box splines.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1992
Accession Number
ADA247105

Entities

People

  • Amos Ron
  • Carl R. de Boor
  • Ronald A. Devore

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Analogs
  • Applied Mathematics
  • Construction
  • Equations
  • Fourier Analysis
  • Functional Analysis
  • Hilbert Space
  • New York
  • Numbers
  • Periodic Functions
  • Polynomials
  • Sequences
  • South Carolina
  • Theorems
  • Two Dimensional
  • United States
  • Wisconsin

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Human-Computer Interaction (HCI).
  • Statistical inference.

Technology Areas

  • Space