Approximation-theoretic analysis of translation invariant wavelet expansions

Author

Liu, Juan ; Moulin, Pierre

Author_Institution

Dept. of Electr. & Comput. Eng., Illinois Univ., Urbana, IL, USA

Volume

1

fYear

2001

fDate

6/23/1905 12:00:00 AM

Firstpage

622

Abstract

It has been observed from image denoising experiments that translation invariant (TI) wavelet transforms often outperform orthogonal wavelet transforms. This paper compares the two transforms from the viewpoint of approximation theory, extending previous results based on Haar wavelets. The advantages of the TI expansion over orthogonal expansion are twofold: the TI expansion produces smaller approximation error when approximating a smooth function, and it mitigates Gibbs artifacts when approximating a discontinuous function

Keywords

approximation theory; function approximation; image processing; wavelet transforms; Gibbs artifacts; Haar wavelets; approximation error approximation; approximation theory; discontinuous function approximation; image denoising experiments; orthogonal expansion; orthogonal wavelet transforms; smooth function; translation invariant expansion; translation invariant wavelet expansions; Approximation error; Autocorrelation; Convolution; Frequency locked loops; Image denoising; Kernel; Multiresolution analysis; Wavelet analysis; Wavelet transforms;

fLanguage

English

Publisher

ieee

Conference_Titel

Image Processing, 2001. Proceedings. 2001 International Conference on

Print_ISBN

0-7803-6725-1

Type

conf

DOI

10.1109/ICIP.2001.959122

Filename

959122