正交小波变换中边界的零延拓及其无失真恢复

Zero Padding of Finite Length Signals for Orthogonal Wavelet Transform and Its Perfect Reconstruction

在有限长信号的小波变换中，一般说来零延拓不是一种好的边界处理方法，但对有些类别的小波，零延拓却能带来处理上的很大方便和收到良好的效果．本文主要探讨了正交小波中低通滤波器ｈｎ的支撑为［０，Ｍ］（即ｈｎ≠０，ｎ＝０，１，…，Ｍ；ｈｎ＝０，ｎ为其它值）的小波变换的边界处理问题，提出了零延拓是其较好的选择．我们首先利用小波变换的性质证明了一个有意义的结论，然后由这个结论证明了这类小波边界零延拓的可完全恢复性，并给出了一种无失真恢复算法，最后把这种方法与其它几种边界处理方法作了比较，指出了这种边界处理的几个优点：一是边界的完全可恢复性；二是完全重构综合滤波器构造的简单性；三是滤波器的性能在边界处的稳定性．

In this paper,we propose zero padding as a boundary processing method for orthogonal wavelet transform with compact support.The perfect reconstruction of zero padding is proved and a perfect reconstruction algorithm is suggested;Zero padding method is compared with several other boundary processing methods and three advantages are pointed out:(1)perfect reconstruction of boundaries;(2)construction simplicity of perfect reconstruction sythesis filter bank;(3)good performance of the filter bank on boundaries.