用多小波对图像分解和重构

与单小波相比较，多小波同时具备诸如紧支性，正交性，对称性等诸多在信号处理中非常重要的良好性质．这决定了多小波是一种优于单小波的信号处理技术．在应用中，对于单小波可以直接利用分解与重构公式对信号进行滤波．但是多小波是用矢量滤波器组对信号进行分毹、重构．滤波对象必须是满足一定要求的矢量信号．因此，在进行多小波分解前必须通过前置滤波器对原始离散信号进行预处理得到初始矢量，然后才能进行多小波变换．同样，对重构后的数据也要进行后处理才能得到需要的结果．本文以GHM多小波为例，实现了对图像的预处理、分解和变换后的重构、后处理过程，并将解压缩后的结果与单小波相比较，获得较好的结果．

IMAGE DECOMPOSITION AND RECONSTRUCTION WITH MULTIWAVELETS

Instead of being generated by one scaling function,multiwavelets scaling functions. In comparison to scalar wavelets, multiwavelets simutaneously are sereval wavelets with several have several advantages such as compact -support ,orthogonality symmetry and so on, which are known to be important in signal processing. Thus, multiwavelets offer single wavelet may the possibility of superior performance for image processing applications. In the application, the directly carry on the filter using the decomposition and the heavy construction formuIa to the signal. But the multiwavelets are carried on the decomposition and the heavy construction with the vector filter group to the signal. The filter object must- be a vector signal satisfied the certain request. Therefore, before carrying the muhiwavelets decomposition, we must pretreat the primitive discrete signal through the predicting filter to obtain the initial vector. After that it can be transformed using the multiwavelets. Similarly, the heavy construction data should be post -process that can obtain the need results. This article takes the GHM multiwavelets as an example, uses it to achieve all of the preprocess, decomposition and reconstruct, post-process after being transformed. At last, we compare the result with the single wavelet,obtain a better result.