多元(M,R)-插值型可加细函数向量的构造

Construction of multivariate interpolating refinable function vectors of type(M,R)

本文提出了一个全新的具有r个分量函数的多元插值型可加细函数向量,即(M,R)-插值型可加细函数向量,这里M是膨胀矩阵,r=|detR|.基于(M,R)-插值型尺度滤波器,我们详细地刻画了(M,R)-插值型可加细函数向量的性质,并得到了尺度滤波器满足k+1阶和规则的充分必要条件.此外,为获得具有对称性的(M,R)-插值型可加细函数向量,我们还给出了相应尺度滤波器的结构.围绕上述理论结果,在本文的最后,我们给出了若干数值构造实例.

In this paper, we shall put forward a generalized notion of multivariate interpolating M-refinable function vectors with multiplicity r = ｜detR｜ that is, interpolating refinable function vectors of type （M, R）. We shall characterize the interpolating refinable function vectors in terms of their interpolatory masks. In addition, the sum rule structure with symmetry property is investigated. To illustrate the results of this paper, the construction algorithm and an interesting bivariate example will be presented.