Compactly Supported Tight Affine Spline Frames in L2(Rd).

Abstract

The theory of RS2 is applied to yield compactly supported tight affine frames (wavelets) in L2(Rd) from box splines. The wavelets obtained are smooth piecewise polynomials on a simple mesh; furthermore, they exhibit a wealth of symmetries, and have a relatively small support. The number of 'mother wavelets', however, increases with the increase of the required smoothness. Two bivariate constructions, of potential practical value, are highlighted. In both, the wavelets are derived from four-direction mesh box splines that are refinable with respect to the dilation matrix.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1996
Accession Number
ADA304488

Entities

People

  • Amos Ron
  • Zuowei Shen

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Computations
  • Computer Science
  • Construction
  • Convolution
  • Data Compression
  • Frequency
  • Frequency Domain
  • Language
  • Mathematics
  • Military Research
  • Periodic Functions
  • Polynomials
  • Standards
  • Symmetry
  • Universities

Readers

  • Approximation Theory.
  • Graph Algorithms and Convex Optimization.