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Numerical stability of biorthogonal wavelet transforms

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Abstract

For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including efficient numerical estimates if the numberL of decomposition levels is small, as well as growth estimates forL → ∞. These estimates allow easy determination of numerical stability directly from the wavelet coefficients. Examples show that many biorthogonal wavelets are in fact numerically well behaved.

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Authors and Affiliations

  1. Department of Mathematics, Iowa State University, 50011, Ames, IA, USA

    Fritz Keinert

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  1. Fritz Keinert
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Keinert, F. Numerical stability of biorthogonal wavelet transforms. Adv Comput Math 4, 1–26 (1995). https://doi.org/10.1007/BF02123471

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  • DOI: https://doi.org/10.1007/BF02123471

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