Mathematical properties of the two-parameter family of 9/7 biorthogonal filters

Author

Tay, David B H ; Marusic, Slaven ; Palaniswami, Marimuthu ; Deng, Guang

Author_Institution

Dept. of Electron. Eng., La Trobe Univ., Vic., Australia

Volume

3

fYear

2004

fDate

23-26 May 2004

Abstract

The family of biorthogonal filters considered here are of lengths 9 and 7 and represent a super-set of the 9/7 pair that is used in the JPEG2000 compression standard. The filters have two vanishing moments that are structurally imposed and possess two degrees of freedom for varying (tuning) the filter characteristics. A study of the mathematical properties of these filters is presented here. Properties from wavelet theory such as convergence of the two-scale equation, Sobolev regularity measure, Riesz bounds and the projection cosine of the approximation subspaces will be evaluated.

Keywords

approximation theory; data compression; filtering theory; filters; image coding; wavelet transforms; 9/7 biorthogonal filters; JPEG2000 compression standard; Riesz bounds; Sobolev regularity measure; degrees of freedom; mathematical properties; projection cosine; subspace approximation; two-scale equation convergence; vanishing moment; wavelet theory; Convergence; Digital filters; Discrete wavelet transforms; Equations; Filtering theory; Low pass filters; Nonlinear filters; Scattering; Transform coding; Watermarking;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 2004. ISCAS '04. Proceedings of the 2004 International Symposium on

Print_ISBN

0-7803-8251-X

Type

conf

DOI

10.1109/ISCAS.2004.1328810

Filename

1328810