Multiresolution analysis on bounded domains for the design of biorthogonal wavelet bases

Author

Coffey, Mark A. ; Etter, Delores M.

Author_Institution

Dept. of Electr. & Comput. Eng., Colorado Univ., Boulder, CO, USA

Volume

50

Issue

3

fYear

2002

fDate

3/1/2002 12:00:00 AM

Firstpage

509

Lastpage

519

Abstract

An axiomatic approach to biorthogonal multiresolution analyzes on bounded domains is presented. The intervalized multiresolution analysis (MRA) leads to a generalized framework within which one can construct biorthogonal wavelet transforms, including many constructions presented in the literature to date. The framework also leads naturally to algorithms for calculating and constraining pertinent properties of both the discrete filters and their corresponding continuous basis functions. Construction of wavelet analysis within the new framework is then illustrated with the design of a basis specifically tailored to reduce the boundary artifacts induced by some wavelet transforms used in image processing

Keywords

filtering theory; image resolution; wavelet transforms; QMF; axiomatic approach; biorthogonal multiresolution analysis; biorthogonal wavelet bases design; biorthogonal wavelet transforms; boundary artifacts reduction; bounded domains; continuous basis functions; discrete filters; discrete multiresolution techniques; image processing; semi-infinite interval; Continuous wavelet transforms; Discrete wavelet transforms; Filtering algorithms; Filters; Image analysis; Image processing; Multiresolution analysis; Wavelet analysis; Wavelet domain; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.984725

Filename

984725