Comparison of wavelets from the point of view of their approximation error
Journal
Proceedings of SPIE - The International Society for Optical Engineering
Journal Volume
3458
Date Issued
1998-12-01
Author(s)
Unser, Michael
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 punished 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 π as the order goes to infinity.
Subjects
Approximation theory | Asymptotics | Daubechies wavelets | Error analysis | Linear approximation | Splines | Wavelet transform
Type
conference paper