线性完全重构的二维滤波器组的Groebner基设计

Design Linear-Phase Perfect Reconstruction Multidimensional Filter Bank Using Groebner Basis

为设计线性完全重构的二维滤波器组,引用了计算代数中的Groebner基方法,根据线性相位条件和完全重构条件,分别设计出二维滤波器组的分析滤波器和综合滤波器的多相元矩阵,给出其参数化形式。根据小波构造理论,利用所设计的分析滤波器组构造出一个对称的纯二维小波。设计结果显示了Groebner基方法的有效性,设计方法更为简单。

To design linear-phase perfect reconstruction two-dimensional filter bank, according to its condition for linear phase and condition for perfect reconstruction, the Polyphase matrix of analysis and synthesis 2D filter banks are designed by using the Groebner basis algorithm of algebra, and the parameterization of filter banks is obtained. By application wavelets theory, a symmetry 2D wavelets is constructed. The results show that this Groebner basis method is valid, and it is more easy than others.