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Decomposition and reconstruction of multidimensional signals by radial functions with tension parameters

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Abstract

The aim of the paper is to construct a multiresolution analysis of L2(IRd) based on generalized kernels which are fundamental solutions of differential operators of the form \(\boldsymbol {\prod }_{\ell = 1}^{m}(-{\Delta }+\kappa _{\ell }^{2}\,I)\). We study its properties and provide a set of pre-wavelets associated with it, as well as the filters which are indispensable to perform decomposition and reconstruction of a given signal, being very useful in applied problems thanks to the presence of the tension parameters κℓ.

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Acknowledgements

We would like to thank the anonymous reviewers for their valuable remarks and suggestions.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università di Milano–Bicocca, via Roberto Cozzi 55, 20125, Milano, Italy

    Mira Bozzini & Milvia Rossini

  2. INSA Toulouse (Institut National des Sciences Appliquées), 135, Avenue de Rangueil, 31077, Toulouse Cedex 4, France

    Christophe Rabut

Authors
  1. Mira Bozzini
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  2. Christophe Rabut
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  3. Milvia Rossini
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Correspondence to Milvia Rossini.

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Communicated by: Robert Schaback

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Bozzini, M., Rabut, C. & Rossini, M. Decomposition and reconstruction of multidimensional signals by radial functions with tension parameters. Adv Comput Math 44, 1003–1040 (2018). https://doi.org/10.1007/s10444-017-9571-7

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  • DOI: https://doi.org/10.1007/s10444-017-9571-7

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