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Compactly supported box-spline wavelets

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Approximation Theory and its Applications

Abstract

A general procedure for constructing multivariate non-tensor-product wavelets that generate an orthogonal decomposition ofL 2(R)s,s s≥1, is described and applied to yield explicit formulas for compactly supported spline-wavelets based on the multiresolution analysis ofL 2(R)s 1≤s≤3, generated by any box spline whose direction set constitutes a unimodular matrix. In particular, when univariate cardinal B-splines are considered, the minimally supported cardinal spline-wavelets of Chui and Wang are recovered. A refined computational scheme for the orthogonalization of spaces with compactly supported wavelets is given. A recursive approximation scheme for “truncated” decomposition sequences is developed and a sharp error bound is included. A condition on the symmetry or anti-symmetry of the wavelets is applied to yield symmetric box-spline wavelets.

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Authors and Affiliations

  1. Center for Approximation Theory Department of Mathematics, Texas A&M University, 77843-3368, College Station, TX

    C. K. Chui & J. D. Ward

  2. Department of Mathematics, University of Duisburg, D-4100, Duisburg, Germany

    J. Stöckler

Authors
  1. C. K. Chui
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  2. J. Stöckler
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  3. J. D. Ward
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Additional information

Partially supported by ARO Grant DAAL 03-90-G-0091

Partially supported by NSF Grant DMS 89-0-01345

Partially supported by NATO Grant CRG 900158.

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Chui, C.K., Stöckler, J. & Ward, J.D. Compactly supported box-spline wavelets. Approx. Theory & its Appl. 8, 77–100 (1992). https://doi.org/10.1007/BF02836340

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  • DOI: https://doi.org/10.1007/BF02836340

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