【作者】 李可维；

【导师】 施保昌；

【作者基本信息】 华中科技大学 ， 计算数学， 2006， 硕士

【摘要】 单小波作为一种成熟的多分辨方法已经在信号处理,图像处理的各个领域得到了极为广泛的应用。然而,在许多情况下,传统单小波的性质不能满足全部需要。比如单小波除Haar小波外不可能同时具有正交性,紧支性,对称性。而多进制小波和多小波能同时具有这些对信号处理十分重要的特性,所以近年来得到了研究者的广泛关注。非正弦类矩阵,主要是Walsh矩阵和斜矩阵,它们一类联系紧密的矩阵,而且均为小波矩阵。本文利用Walsh矩阵和斜矩阵构造出两类小波,第一类是多进制的Haar和斜Haar小波;第二类是基于参数斜矩阵的多进制多小波,这两类小波的滤波器组都可由Walsh矩阵和斜矩阵得到。文中给出了这两类小波的构造方式、证明过程、小波的分解重构算法、小波基的选择。本文的第一个仿真实验将多进制的Haar和斜Haar小波用于图像纹理分类实验,比较了此类多进制Haar小波的分类结果,加快了这类小波的分解速度并根据纹理图像的特点利用多进制斜Haar小波滤波器组提取的纹理特征进行分类实验,给出了实际应用中各种情况下对小波基选择和特征量个数选择的分析。第二个实验是将基于参数斜矩阵的多进制多小波用于在图像去噪中。这类多进制多小波的滤波器组矩阵由参数斜矩阵生成,构造方便,并能通过对参数的适当选择使滤波器系数更具灵活性。更多还原

【Abstract】 A variety of wavelets are widely used in the fileds of signal processing and image processing as a mature Multi-Resolution Analysis(MRA) method.However,in many situations, traditional wavelets can not meet the entire need.For example,all traditional wavelets except Haar wavelet do not have all qualities of wavelets. Comparing traditional wavelets,the M-bond wavelets and multiwavelets can have all the qualities of wavelets.So they arouse many attentions of the researchers.Walsh matrix and Slant matrix are the non-sinusoidal matrixes which have a close relationship with each other.They are both the wavelet matrixes.We construct two kinds of wavelet.One is M-Band Haar wavelet and Slant Haar Wavelet.The other is M-bond multiwavelet based on parametric slant matrix.The filter banks of these M-bond multiwavelets are conveniently generated by parametric Slant matrixes.The filter banks are very flexible by being choosed some proper parameters.This paper also has two numerical tests.In the first test, the paper decompose texture images into some parts with M-Band Haar wavelet and Slant Haar Wavelet,then extract texture features and classify texture based on the minimum distance classifier.In the other test, the paper apply M-bond multiwavelet base on parametric slant matrix to image denoising based on threshold and get a satisfactory result.更多还原