Optimization design of biorthogonal wavelets for embedded image coding

We present here a simple technique for parametrization of popular biorthogonal wavelet filter banks (BWFBs) having vanishing moments (VMs) of arbitrary multiplicity. Given a prime wavelet filter with VMs of arbitrary multiplicity, after formulating it as a trigonometric polynomial depending on two free parameters, we prove the existence of its dual filter based on the theory of Diophantine equation. The dual filter permits perfect reconstruction (PR) and also has VMs of arbitrary multiplicity. We then give the complete construction of two-parameter families of 17/11 and 10/18 BWFBs, from which any linear-phase 17/11 and 10/18 BWFB possessing desired features could be derived with ease by adjusting the free parameters. In particular, two previously unpublished BWFBs for embedded image coding are constructed, both have optimum coding gains and rational coefficients. Extensive experiments show that our new BWFBs exhibit performance equal to Winger's W–17/11 and Villasenor's V–10/18 (superior to CDF–9/7 by Cohen et al. and Villasenor's V–6/10) for image compression, and yet require slightly lower computational costs.