基于Mallat算法的图像边界问题的研究

首先介绍了一维信号边界对称延拓方式及图像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，研究了当高、低通滤波器长度为偶数，且关于1／2对称时，图像能够精确重构的边界延拓问题，并给出了图像的小波变换及边界对称延拓的步骤。最后，通过仿真实例验证了该对称边界延拓方式能够保证图像在小渡变抉中精确重构。

Study of image boundary problem based on mallat algorithm

At first the method of symmetric boundary extension about one-dimensional signal and the decomposition and reconstruction algorithm of fast biorthogonal wavelet transform about image are introduced. Based on the method of boundary extension about one-dimensional signal, the method of boundary extension about image is studied under the condition that high and low filters have an even number of non-zero samples and are symmetric about 1/2, At the same time, the steps of wavelet transform and boundary extension for image is given. This method of boundary extension can guarantee that image will be reconstructed accurately in Mallat algorithm. The validity of the proposed boandary extension method of image is illustrated via the simulation results.