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Polyharmonic multiresolution analysis: an overview and some new results

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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.

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Authors and Affiliations

  1. INSA, IMT, Université de Toulouse, 135 avenue de Rangueil, 31077, Toulouse Cedex 4, France

    Christophe Rabut

  2. Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via Cozzi 53, 20125, Milan, Italy

    Milvia Rossini

Authors
  1. Christophe Rabut
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  2. Milvia Rossini
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Correspondence to Christophe Rabut.

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Rabut, C., Rossini, M. Polyharmonic multiresolution analysis: an overview and some new results. Numer Algor 48, 135–160 (2008). https://doi.org/10.1007/s11075-008-9173-z

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  • DOI: https://doi.org/10.1007/s11075-008-9173-z

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