高阶平衡多小波的Groebner基构造

Construction of High-Order Balanced Multiwavelets Using Groebner Basis

为构造出图像处理中无需预滤波的平衡多小波，研究高阶平衡多小波的平衡性，并结合其对称性和正交性，构成一组以平衡多小波的滤波器系数为未知数的高阶多元多项式非线性方程组、利用计算代数中的Groebner基算法，获得了1～3阶平衡多小波滤波器组的全部系数，并绘制了它们的波形图．从波形图可见，多小波的平衡阶数越高，其波形越光滑，但计算难度显著加大．

To construct balanced multiwavelets which can avoid prefiltering in image processing, through a study of performance of balance in balanced multiwavelets, combing its symmetry and orthogonality, a high-order multivariable polynomial system is formed, where the coefficients of balanced multiwavelets are variables. By the application of Groebner basis algorithm in computational algebra, a group of coefficients of the 1- 3 order balanced multiwavelets filter bank are obtained, and its oscillograms plotted. The oscillograms show that the higher the order of balanced wavelets, the smoother its waveform becomes, but the difficulty in computation is obviously increased.