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Numerical Algorithms

, Volume 48, Issue 1–3, pp 135–160 | Cite as

Polyharmonic multiresolution analysis: an overview and some new results

  • Christophe Rabut
  • Milvia Rossini
Original Paper

Abstract

This paper first presents a condensed state of art on multiresolution analysis using polyharmonic splines: definition and main properties of polyharmonic splines, construction of B-splines and wavelets, decomposition and reconstruction filters; properties of the so-obtained operators, convergence result and applications are given. Second this paper presents some new results on this topic: scattered data wavelet, new polyharmonic scaling functions and associated filters. Fourier transform is of extensive use to derive the tools of the various multiresolution analysis.

Keywords

Polyharmonic splines Wavelets MRA filters 

Mathematics Subject Classifications (2000)

65D07 65T60 

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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.INSA, IMTUniversité de ToulouseToulouse Cedex 4France
  2. 2.Dipartimento di Matematica e ApplicazioniUniversità di Milano BicoccaMilanItaly

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