一种基于提升格式的双正交小波设计方法及应用

提升格式是一种新的小波构造方法，它是因构造紧支的第二代小波之需而产生的。Sweldens等人提出的提升格式设计方法只能设计基于Lazy小波的插值小波，为了满足各种应用需要，提出了一种基于任意双正交小波，而非仅针对Lazy小波的增加小波消失矩的新算法。利用小波消失矩和与其对应滤波器在z=1处零点阶数之间的关系，通过求解一组简单的线性方程组来设计基于任意双正交小波的提升系数；根据最佳提升格式的唯一性，给出了求最佳提升系数的迭代算法。

A Novel Design of Biorthogonal Wavelets Based on the Lifting Scheme and Its Application

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.