The Lifting Scheme Based on the Second Generation Wavelets

0 IntroductionTfhaect w tahvaetl e,t“ twheaovreyle thsas ar mea noypt ip rmoaple rbtaiseess w fhoirch coremspurltesisnintghe,esti mating,and recoveringfunctions”[1]. The traditional wave-let defined as the dyadic translates and dilates of one particularfunction, which relies on the Fourier transform, suitable forregular sampling data. But it is helpless for the application ofli mit region,curve surface and not-even sampling. Then W.Sweldens[1]and other researchers develop some other method…

The lifting scheme based on the second generation wavelets

The lifting scheme is a custom design construclion of Biorthogonal wavelets, a fast and efficient method to realize wavelet transform,which provides a wider range of application and efficiently reduces the computing time with its particular frame. This paper aims at introducing the second generation wavelets, begins with traditional Mallat algorithms, illustrates the lifting scheme and brings out the detail steps in the construction of Biorthogonal wavelets. Because of isolating the degrees of freedom remaining the biorthogonality relations, we can fully control over the lifting operators to design the wavelet for a particular application, such as increasing the number of the vanishing moments.