矩条件参数化3带对称正交小波

Parametrizing rank 3 symmetric orthogonal wavelets by discrete moments

对具有消失矩性质的3带对称正交小波进行参数化,给出正交小波的几个重要性质,同时讨论滤波器系数长度、对称中心点、消失矩和离散矩之间的联系,通过放弃线性方程组中的几个消失矩条件来引入尺度函数的三阶离散矩作为参数。给出了构造3带正交对称小波滤波器的约束方程组的算法,计算得出一组含有1个参数的9长滤波器系数的准确表达式。本文给出的构造方法算法易于理解和推广,求解过程相对简单。

The paper discuss parametrizations of filters corresponding to with several vanishing moments. After recalling some properties of rank 3 orthogonal wavelets, relations between the number of filters, symmetry, vanishing moments and discrete moments are discussed. The paper give up some vanishing moment conditions, which correspond to linear constraints on the filters, and introduce discrete moments of the filters as parameters. An algorithm is provided for constructing system equationns for rank 3 orthogonal wavelets filter coefficients. Finally, the associated several families examples with one-parameter are presented explicitly. This paper compute one example using algorithm, the algorithm is easy to be understood and generalize, the process of computing are easier.