Mathematical properties of the two-parameter family of 9/7 biorthogonal filters
D.B.H. Tay, Slaven Marusic, Marimuthu Swami Palaniswami, Guang Yi Deng · 2004
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.