双正交偶对称小波的数据量保持型边界对称延拓方法

Boundary symmetric extension methods with length unchanged for biorthonormal wavelet with even symmetry

在Mallat算法的理论框架下,以双正交偶对称小波为基础,重点讨论了以边界为中心对称的延拓方法,详细推导了任意信号起点、任意信号长度的分解与重构公式,并总结出了此方法下实现小波变换的一般规程.以Haar双正交小波给出实例,计算结果表明,在保持信号长度不变的情况下,按本延拓方式能够实现完全重构.

Based on the theory of Mallat algorithm, the boundary symmertric extension methods for biorthonormal wavelet with even sysmmetry are studied. And the wavelet decomposition and the perfect reconstruction are implement-ed, whatever the lenghth of the signal or the start of the signal is odd or even. The general process of the wavelet transform with boundary symmertric extension methods is derived. An example using Haar bi-orthogonal wavelet is given to show that the proposed method preserves the perfect reconstruction while keeping the signal length unchanged.