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The generalized matrix product and the wavelet transform

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Abstract

This paper provides a new formulation of wavelet transforms in terms of generalized matrix products. After defining the generalized matrix product, a fast algorithm using parallelism for compactly supported wavelet transforms that satisfym-scale scaling equations form ≥ 2 is established. Several special examples, such as the Fourier-wavelet matrix expansion and wavelet decompositions and reconstructions, that demonstrate that the new formulation and algorithm offer unique advantages over existing wavelet algorithms are provided.

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Authors and Affiliations

  1. Center for Computer Vision Research, University of Florida, 32611, Gainesville, FL, USA

    Huixia Zhu & Gerhard X. Ritter

Authors
  1. Huixia Zhu
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  2. Gerhard X. Ritter
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Additional information

This research was supported in part by U.S. Air Force contract F08635-89-C-0134.

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Zhu, H., Ritter, G.X. The generalized matrix product and the wavelet transform. J Math Imaging Vis 3, 95–104 (1993). https://doi.org/10.1007/BF01248405

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  • DOI: https://doi.org/10.1007/BF01248405

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