Z上框架小波包的构造方案及算法实现（英文）

Construction of Framelet Packets on Z and Algorithm Implementation

为了进一步推动小波理论的应用,近些年来在离散数据环境中开始了对框架小波(也称为framelets)和框架小波包的研究工作.在l^2(Z)中构造J-级框架小波包的方法已经由鲁大勇和易华给出.然而,如何去使用这类小波包的细节却没有给出.为了进一步丰富由鲁和易提出的J-级框架小波包理论体系,该文给出了快速的分解和重构算法,运用该算法可以建立不同尺度层之间小波框架系数的关系.另外,为了方便该类框架小波包的应用,文中给出了l^2(Z)中一些实用框架小波包的具体数据.文中最后通过一个数值实验展示了该类框架小波包的完美重构性质.

In order to facilitate the use of wavelets, the study on frame wavelets (also called framelets) and framelet packets in digital setting has been addressed in recent years. An approach to construct a class of J-stage framelet packets for l^2(Z) is given by Lu and Yi. However, the detailed results on how to use them are missing. To further improve the theoretical system of J-stage framelet packets for l^2(Z), by following the work of Lu and Yi, the fast decomposition and reconstruction algorithms are given in this paper, with which one can establish the relationship of coefficients between different stages. For the convenience of using, the detailed data of framelet packets for l^2(Z) when the number n of mother framelet ranges from 1 to 4 are constructed. Finally, a numerical experiment is given to illustrate the perfect reconstruction of framelet packets.