LIFTING CONSTRUCTION OF SPLINE DYADIC WAVELET FILTERS WITH ANY NUMBER OF VANISHING MOMENTS

摘要

The dyadic lifting schemes, which generalize Sweldens lifting schemes, have been applied to design dyadic wavelet with higher number of vanishing moments. But the existing dyadic lifting methods cannot give the free parameters (i.e. lifting factors) explicitly under vanishing moment constraints, and the exact vanishing moments of the lifted wavelet is unknown a priori. This paper provides a solution of these problems for spline dyadic wavelets. It proposes a novel constructive method for lifting constructing spline dyadic wavelets with desirable numbers of vanishing moments. This new lifting construction scheme can be applied to design spline dyadic wavelet filters with any number of vanishing moments starting from one single dyadic wavelet with 1 or 2 vanishing moments. Its computational advantage is that the lifting factor parameters can be chosen and given explicitly under vanishing moment constraints. At the end of this paper, some spline dyadic wavelet filters are designed by using our method.