多小波与平衡多小波的理论和设计

Theory and Design of Multiwavelet and Balanced Multiwavelet

多小波成为研究的热点 ,部分原因是因为它可同时拥有正交对称和紧支撑性质。然而在应用于实际进行离散多小波变换的实现时 ,必须对它进行具体的预滤波 ,这一过程有时会破坏所设计的多小波已有的重要性质。为弥补这一缺陷 ,平衡多小波被引入 ,这种多小波在进行信号处理时可以不需要进行预滤波 ,且显示良好的应用前景。为了更好的理解和应用它 ,本文对平衡多小波理论研究予以综述 ,并展望它今后的发展。

Multiwavelets becames a focus of research partly because they made possible the construction of wavelet systems that are simultaneously orthogonal, symmetric, and compactly supported, which is not possible for any real valued scalar wavelets. However, it became clear that the implementation of the discrete multiwavelet transform required the design of specialized prefilters, which sometimes destroys the very properties a multiwavelet is designed to have. Recently, a new subclass of balanced multiwavelet needing no prefiltering procedure has been proposed and have show better prospects in application. In order to understand and applied it moer better, we review the theory and design of balanced multiwavelet, and point out some interesting issues in future ressearch.