高阶消失矩的Hermite三次样条小波

由于消失矩在小波应用中具有重要作用，本文在借鉴Jia和Liu工作的基础上，构造了支集在-2，2]内具有6阶，7阶消失矩的对称及反对称Hermite三次样条函数峨，峨，并且证明它们的整平移具有如（R）稳定性．首先说明在一定意义下所有支集在内-1，1]，对称和反对称的小波均为Jia所求解小波的常数倍．其次，尝试按照Jia的标准构造支集在-2，2]上的具有高阶消失矩的小波，遗憾的是它们的整平移不具有稳定性；最后，通过改变了标准，得到了理想的结果。

Hermite Cubic Spline Wavelet with High Order Vanishing Moments

Because vanishing moments are important in wavelets applications, this paper constructs Hermite spline wavelets ψ1 （x） and ψ2 （x） with compact supports on -2, 2]. They have vanishing moments of order 6 and 7 respectively, as well as symmetric and antisymmentric properties. In addition, it is proved that the integer translations of wavelets are L2 （R） stable. All these work are motivated by Jia＇s paper. First, we show that all symmetric and antisymmetric wavelets with compact supports on - 1,1 ] are times the wavelets given by Jia in some sense; Second, we try to find wavelets with vanishing moments of higher order and compact supports on - 2,2 ], according to Jia＇ s standard. However, there is a problem in integer translations stability. Finally, we receive the desired result by changing the standard.