平衡多小波的Grbner基构造及其应用

Grbner Basis Construction and Application of Balanced Multiwavelet

平衡多小波由于可避免预滤波而成为小波分析的研究热点,对已有不平衡多小波进行平衡,常会丢失多重尺度函数的对称性.通过对平衡多小波的平衡特性进行研究,结合正交性、对称性,构造一组由小波系数构成的多元多项式方程组,利用Grbner基方法求解出2阶平衡多小波的滤波器系数.采用2阶平衡多小波对图像进行压缩处理,取得了良好效果.

Balanced multiwavelet which can avoid prefiltering is an active area of wavelet research. The balancing of unbalanced multiwavelet will destroy its symmetry of multiscale functions. Through studying balance performance of balanced multiwavelet and combining its orthogonality and symmetry a multivariable polynomial system is constructed. Based on the application of Groebner basis, a group of filter coefficients of 2-order balanced multiwavelet are obtained. The image is compressed by 2-order balanced orthogonal multiwavelet. The experiments show that the effect of coding is better.