平行六边形上的周期正交小波

Periodic Orthogonal Wavelets Defined on Parallel Hexagon

通过构造三向剖分下平行六边形上的周期多尺度分析,利用三向剖分下平行六边形上的离散Fourier变换方法,给出一类以平行六边形为周期的非张量积二元正交小波的构造方法.构造的正交尺度函数和小波的两尺度方程中只包含4项,因而相应的分解和重构算法也只有4项.构造方法易于实现、计算简单并具有一般性.

First, we constructed a periodic multiresolution analysis about the parallel hexagon. Then, using the discrete Fourier transform over 3-direction partition domains, we constructed a kind of bivariate periodic non-tensor-product orthogonal wavelets defined on parallel hexagons. There are only 4 terms in the corresponding refinement equations of the orthogonal scaling functions and the wavelets (and so do the decomposition and reconstruction algorithms). The method presented here is general which is simple for implementation.