Shift-invariant spaces from rotation-covariant functions

Brigitte Forster, Thierry Blu, Dimitri Van De Ville, Michael Unser

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We consider shift-invariant multiresolution spaces generated by rotation-covariant functions ρ in R2. To construct corresponding scaling and wavelet functions, ρ has to be localized with an appropriate multiplier, such that the localized version is an element of L2 (R2). We consider several classes of multipliers and show a new method to improve regularity and decay properties of the corresponding scaling functions and wavelets. The wavelets are complex-valued functions, which are approximately rotation-covariant and therefore behave as Wirtinger differential operators. Moreover, our class of multipliers gives a novel approach for the construction of polyharmonic B-splines with better polynomial reconstruction properties.

Original languageEnglish
Pages (from-to)240-265
Number of pages26
JournalApplied and Computational Harmonic Analysis
Volume25
Issue number2
DOIs
StatePublished - Sep 2008

Keywords

  • Complex wavelets
  • Multiresolution
  • Riesz basis
  • Rotation covariance
  • Scaling functions
  • Shift-invariant spaces
  • Two-scale relation

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