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

Michael A. Unser; Thierry Blu

doi:10.1117/12.328141

Translator Disclaimer

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); doi: 10.1117/12.328141; https://doi.org/10.1117/12.328141

ACCESS THE FULL ARTICLE

PERSONAL SIGN IN
Full access may be available with your subscription

Email or Username Forgot your username?

Password Forgot your password?

Show

Remember Email/Username on this computer

Remember Password

No SPIE account? Create an account

Institutional Access:

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $14.40

Non-members: $18.00 ADD TO CART

Show All Keywords

Keywords/Phrases

Search In:

Publication Years