A wavelet filter performance criterion

Frederic Nicolier; Frederic Truchetet

doi:10.1117/12.581231

Abstract

In this paper, an objective criterion on wavelet filters in proposed. Wavelet transforms are used in number of important signal and image industrial processing tasks including image coding and denoising. The choice of the wavelet filter bank is is very important and is directly linked to the efficiency of the application. Some criteria have been proposed such as regularity, size of the support of the wavelet and number of vanishing moments. The size of the wavelet support increases with the number of vanishing moments. The wavelet regularity is important to reduce the artifacts. The choice of an optimal wavelet is thus the result of a trade-off between the number of vanishing moments and artifacts. But there is only a partial correlation between filter regularity and reconstructed image quality. The proposed criterion is composed of two indexes. The first one is a frequency index computed from the aliasing of the filters. The second is a spatial index computed from the spread of the coefficients in spatial domain. From these indexes a filter set can be represented by a point in a criteria-plan. The abscissa is given by the frequency index and the ordinate by the spatial index. The quality of a wavelet filter bank is a trade-off between frequency and spatial quality. So the quality of a wavelet filter bank can be assessed from the position of the corresponding point in the criteria-plan. The coding and denoising performances are estimated for various filters (including orthogonal splines and Daubechies). These performances are connected to the indexes of each filter bank. The results show that the two proposed indexes allow : 1/ a good estimation of the coding and denoising performances of the wavelet filters, and 2/ an objective comparison of the filters. Some clues on the connection between our indexes and the kernel size in the Heisenberg-Gabor formula are also given.

Citation Download Citation

Frederic Nicolier, Frederic Nicolier, Frederic Truchetet, Frederic Truchetet, } "A wavelet filter performance criterion", Proc. SPIE 5607, Wavelet Applications in Industrial Processing II, (1 November 2004); doi: 10.1117/12.581231; https://doi.org/10.1117/12.581231

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
or Institutional Sign In via Shibboleth

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