Comparison of wavelets from the point of view of their approximation error

Michael A. Unser; Thierry Blu

doi:10.1117/12.328141

19 October 1998 Comparison of wavelets from the point of view of their approximation error

Michael A. Unser, Thierry Blu

Proceedings Volume 3458, Wavelet Applications in Signal and Imaging Processing VI; (1998) https://doi.org/10.1117/12.328141
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

Abstract

We present new quantitative results for the characterization of the L₂-error of wavelet-like expansions as a function of the scale a. This yields an extension as well as a simplification of the asymptotic error formulas that have been published previously. We use our bound determinations to compare the approximation power of various families of wavelet transforms. We present explicit formulas for the leading asymptotic constant for both splines and Daubechies wavelets. For a specified approximation error, this allows us to predict the sampling rate reduction that can obtained by using splines instead Daubechies wavelets. In particular, we prove that the gain in sampling density (splines vs. Daubechies) converges to (pi) as the order goes in infinity.

Citation Download Citation

Michael A. Unser and Thierry Blu "Comparison of wavelets from the point of view of their approximation error", Proc. SPIE 3458, Wavelet Applications in Signal and Imaging Processing VI, (19 October 1998); https://doi.org/10.1117/12.328141

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