A new class of biorthogonal wavelet systems for image transform coding

We construct general biorthogonal Coifman wavelet systems, a new class of compactly supported biorthogonal wavelet systems with vanishing moments equally distributed for a scaling function and wavelet pair. A time-domain design method is employed and closed-form expressions for the impulse responses and the frequency responses of the corresponding dual filters are derived. The resulting filter coefficients are all dyadic fractions, which is an attractive feature in the realization of multiplicationfree discrete wavelet transform. Even-ordered systems in this family are symmetric, which correspond to linear-phase dual filters. In particular, three filterbanks (FB’s) in this family are systematically verified to have competitive compression potential to the 9-7 tap biorthogonal wavelet FB by Cohen et al., which is currently the most widely used one in the field of wavelet transform coding. In addition, the proposed FB’s have much smaller computational complexity in terms of floating-point operations required in transformation, and therefore indicate a better tradeoff between compression performance and computational complexity.