基于小波变换的图像边界问题的研究

首先简要地介绍了一维信号对称边界延拓方式及二维信号双正交小波分解重构算法，然后在一维信号边界延拓方式的基础上，研究了在小波变换过程中，当高、低通滤波器长度为奇数且关于0对称时，数字图像能够精确重构的边界延拓问题。给出了数字图像的小波变换及边界延拓的步骤。最后，通过仿真实例验证了该对称边界延拓方式能够保证数字图像在小波变换中精确重构。

Boundary problem of image based on wavelet transform

The method of symmetric boundary extension about one-dimensional signal and the decomposition and reconstruction algorithm of fast biorthogonal wavelet transform about two-dimensional signals are introduced.Based on the method of boundary extension about one-dimensional signal,the method of boundary extension about digital image is studied under the condition that high and low filters have an odd number of non-zero samples and are symmetric about zero.At the same time,the steps of wavelet transform and boundary extension for digital image are given.This method of boundary extension can guarantee that digital image will be reconstructed accurately in wavelet transform.The validity of the proposed boundary extension method about digital image is illustrated by the simulation results.