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Orthogonal and Nonorthogonal Multiresolution Analysis, Scale Discrete and Exact Fully Discrete Wavelet Transform on the Sphere

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Abstract.

Based on a new definition of dilation a scale discrete version of spherical multiresolution is described, starting from a scale discrete wavelet transform on the sphere. Depending on the type of application, different families of wavelets are chosen. In particular, spherical Shannon wavelets are constructed that form an orthogonal multiresolution analysis. Finally fully discrete wavelet approximation is discussed in the case of band-limited wavelets.

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Authors and Affiliations

  1. W. Freeden, Geomathematics Group,University of Kaiserslautern, D-67653 Kaiserslautern, Germany, 3049, GERMANY

    W. Freeden

  2. M. Schreiner, Geomathematics Group,University of Kaiserslautern, D-67653 Kaiserslautern, Germany, 3049, GERMANY

    M. Schreiner

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  1. W. Freeden
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  2. M. Schreiner
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Additional information

June 18, 1996. Date revised: January 14, 1997.

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Freeden, W., Schreiner, M. Orthogonal and Nonorthogonal Multiresolution Analysis, Scale Discrete and Exact Fully Discrete Wavelet Transform on the Sphere. Constr. Approx. 14, 493–515 (1998). https://doi.org/10.1007/s003659900087

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  • DOI: https://doi.org/10.1007/s003659900087

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