类coif插值小波的构造及应用

Construction of coiflet like interpolating biorthogonal wavelets and its application

介绍了一族类coif插值双正交小波的构造方法 ,该族小波具有以下特点 :基本尺度函数和小波函数及其对偶都是对称、紧支的 ,因此相应滤波器是具有线性相位的FIR滤波器 ;基本小波与其对偶以及对偶尺度函数都具有 2N阶消失矩 ,前者利于数据压缩 ,后者利于数据逼近 ;对偶尺度函数是插值的 ,插值性更利于数据逼近 .由于这些特点 ,此族小波更适合在计算机图形学中用于建立参数曲线和曲面的多分辨表示 .文中对N =1,N =2给出了具体的滤波器系数 ,并用这些滤波器对一个样条参数曲线建立了多分辨表示 .

The construction method for a family of coiflet like interpolating biorthogonal wavelets is given. It has three attractive characteristics for building the hierarchical multiresolution representation of parametric curves and surfaces in computer graphics. First, the scaling function and the wavelet function and their respective dual are all symmetric and compactly supported so that the corresponding filters are all FIR with linear phase. Second, the two wavelets and the dual scaling function have 2N vanishing moments, which contributes to data compression and data approximation. Third, the dual scaling function is interpolating, which again is helpful for data approximation. The concrete filters are given for the case of  N= 1 and  N= 2, with which we build the multiresolution representation of a cubic spline curve. The result shows that this family of wavelets is much suitable for the multiresolution representation of parameteric curves.