Title :
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
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;
Conference_Titel :
Circuits and Systems, 2004. ISCAS '04. Proceedings of the 2004 International Symposium on
Print_ISBN :
0-7803-8251-X
DOI :
10.1109/ISCAS.2004.1328810
