离散空间中正交小波分解重构算法的实现

Realization of decomposition and reconstruction algorithms for discrete orthogonal wavelets

针对目前离散空间中分解重构算法的过程较为复杂,主要研究离散空间中周期小波和非周期小波分解重构算法的实现。首先证明离散空间中的多层小波分解重构算法可以按照Mallat分解重构算法的塔式结构实现,从而将离散序列空间与函数空间中的小波理论联系起来;其次,举例说明离散空间中的分解重构算法比函数空间中的Mallat分解重构算法在滤波器的选择上更加灵活;最后,数值结果表明基于离散小波对信号进行处理在很多应用中可以取得更好的效果。

In view of the complex process of the cmTent algorithms, this paper mainly studied the realization of decomposition and reconstruction algorithms for periodic and nonperiodie wavelets in discrete spaces. Firstly, one proved that the mnhilevel algorithms could be realized by pyramid frame as Mallat algorithms, which connected the wavelet theory of the discrete se- quence spaces to that of the function spaces. Then, it took an example to show that the decomposition and reconstruction algo- rithms in discrete spaces were more flexible than Mallat algorithms in function spaces. Finally, numerical experiments show better effects of discrete wavelets in some aDDlications of signal ~rocessin~ .