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Proceedings Paper

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

Paper Details

Date Published: 19 October 1998
PDF: 8 pages
Proc. SPIE 3458, Wavelet Applications in Signal and Imaging Processing VI, (19 October 1998); doi: 10.1117/12.328141
Show Author Affiliations
Michael A. Unser, Swiss Federal Institute of Technology (Switzerland)
Thierry Blu, Swiss Federal Institute of Technology (Switzerland)

Published in SPIE Proceedings Vol. 3458:
Wavelet Applications in Signal and Imaging Processing VI
Andrew F. Laine; Michael A. Unser; Akram Aldroubi, Editor(s)

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