高正则非张量积二维小波的Gr(o)bner基构造

为构造非张量积二维小波，在分析二维小波与滤波器组关系的基础上，研究了小波高正则性的务件，并将其转换成一个关于二维滤波器组系数的高阶多元多项式方程组．由于构成这种方程组的方程的未知数和项数都太多，求解它是一个非常困难的问题，因此采用二维小波滤波器组的阶因式分解表示，将待求的高阶多元多项式方程组分解为两个子方程组，应用计算代数中的Grobner基算法分别求解出两个子方程组的Grobner基，进而求解出2～3正则阶的小波滤波器组的全部参数，最终构造出了图像处理中所需要的正交对称的非张量积二维小波．

Construction High Regular No Tensor Product 2-D Wavelets Using Grober Basis

To construct no tensor product 2D wavelet, after analyzing the relation between 2D wavelet and filter banks, we study the regularity condition which the high-regular wavelet must satisfy. Then it is made up of a highorder multivariable polynomial system . But this polynomial system has too many variables and items to be solved. The order-factorable function of 2D wavelet filter banks is used, and the high-order multivariable polynomial system is decomposed to two subsystems, all coefficients of 2 - 3 regular wavelet filter banks are obtained by Grobner bases algorithm. So we have constructed the orthogonal symmetry 2D wavelet which is needed in image processing.