基于多分辨算法的小波框架构造

发布时间：2018-03-15 10:53

本文选题：小波双框架　切入点：统一对称　出处：《北京化工大学》2015年硕士论文　论文类型：学位论文

【摘要】：在工程学应用中使用小波变换时,人们往往避开构造小波基的过程,而是在多分辨算法中使用现有的小波基,因此小波基的构造在一段时间内获得了人们的追捧。本文具体对统一对称的小波双框架的构造进行研究,主要目的是为了用此种类型的滤波器组来解决表面多分辨率处理中的特殊端点问题。对于整个构造过程来说,滤波器组的参数化表示是一个关键环节,本文使用模板形式实现多分辨算法,从最简单的模板表示形式开始,通过不断地交替使用提升格式,来实现简单模板表示的复杂化,其中模板越复杂,获得理想滤波器组的概率越大。本文通过将模板推导为多分辨算法形式,来获取滤波器组的参数化表示。根据混合酉扩展原理的条件,可以针对滤波器组构造一系列方程组,通过求解方程组可以获得参数的实例,而对于带有三个小波滤波器组的小波双框架而言,其构造的方程组结构很复杂,以致于消元法不能直接对其求解,为了解决这一问题,本文采用先对一部分参数进行实例化,然后再使用消元法对方程组进行简化,如此反复进行,直到所有参数都被实例化,这样在一定程度上减小了处理过程中的计算量。对于构建多分辨算法模板部分,本文分为了三种情况进行了讨论,以致于产生了三种类型的小波双框架,并对每种类型的小波双框架进行了相应的对称性证明,获得了对应类型的一个实例。最后,本文对基于小波框架变换的分裂布雷格曼算法进行了简要的概括,并对其在图像去模糊中的运用进行了仿真实验,对比了每种类型滤波器组的实验效果。
[Abstract]:When using wavelet transform in engineering applications, people often avoid the process of constructing wavelet bases, but use existing wavelet bases in multi-resolution algorithms. Therefore, the construction of wavelet bases has been popular for a period of time. In this paper, the construction of unified symmetric wavelet double frames is studied. The main purpose of this paper is to solve the special endpoint problem in surface multi-resolution processing by using this kind of filter banks. The parameterized representation of filter banks is a key step in the whole construction process. In this paper, we use the template form to realize the multi-resolution algorithm, starting with the simplest template representation, we use the lifting format alternately to realize the complexity of the simple template representation, and the more complex the template, the more complex the template is. The higher the probability of obtaining ideal filter banks, the more parameterized representation of filter banks can be obtained by deducing the template as a multi-resolution algorithm. According to the condition of mixed unitary expansion principle, a series of equations can be constructed for filter banks. Examples of parameters can be obtained by solving equations, but for wavelet biframes with three wavelet filter banks, the structure of the equations constructed by them is so complex that the elimination method cannot solve them directly. In order to solve this problem, In this paper, some parameters are instantiated, then the equations are simplified by means of elimination method, which is repeated until all parameters are instantiated. In this way, the computation in the processing process is reduced to a certain extent. For the part of constructing the multi-resolution algorithm template, this paper discusses three kinds of cases, resulting in three types of wavelet double frames. The corresponding symmetry of each type of wavelet biframe is proved, and an example of the corresponding type is obtained. Finally, the split Bregman algorithm based on wavelet frame transform is briefly summarized in this paper. Simulation experiments are carried out on the application of the filter banks in image de-blurring, and the experimental results of each type of filter banks are compared.
【学位授予单位】：北京化工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O174.2

【共引文献】