一种二元紧支集非张量积小波的构造方法

Construct method of bivariate non-tensor product prewavelet with compactly support

从 型三角剖分上的二元可细分的B样条基出发,给出函数属于小波空间的充要条件;利用此条件,构造出小波空间上的4个紧支集、对称的不可分离的连续函数;证明了其中有3个函数的平移形成小波空间的Riesz基.从而得到了 型三角剖分上的紧支集、对称的非张量积预小波.

From theB-spline basis in Ⅰ triangular partition, at first, we got a sufficient and necessary condition under which the function belongs to wavelet space; secondly, by means of this condition, we constructed four non-tensor product compactly supported continuous functions with symmetry; furthermore we demonstrated there are three functions whose shifts form Riesz basis. Therefore we have obtained bivariate non-tensor product prewavelet with compactly support and symmetry in Ⅰ triangular partition.