A Novel Design of Biorthogonal Wavelets Based on the Lifting Scheme and Its Application
Ying Li · Journal of Institute of Command and Technology · 2003
Lifting scheme is a new method of constructing wavelets, and it's developed from the need of constructing the compactly supported second generation wavelets. The method introduced by sweldens can only design the interpolating wavelets based on lazy wavelets. For the various needs, a novel algorithm that is used to lift the vanishing moments of wavelet from arbitrary biorthogonal wavelets, and not only from Lazy wavelet, is proposed. It is based on the relationship between the vanishing moments of the wavelet and multiple of zeros of z=1 and only needs to solve simple linear equations to obtain the lifting coefficients. Moreover, the shortest lifting scheme and its uniqueness are introduced, from which an iterative algorithm for designing the lifting scheme is presented.