a进制Shearlet框架的构造

发布时间：2018-03-23 06:20

本文选题：辅助函数　切入点：a进制　出处：《北方民族大学》2017年硕士论文　论文类型：学位论文

【摘要】：Shearlet变换通过对基函数缩放、剪切和平移仿射变换生成具有不同特征的剪切波函数,对奇异曲线和曲面的高维信号具有最优逼近特性,故可以更好地捕捉图像边缘信息.特别是Shearlet框架,由于同时具有多分辨分析、各向异性、方向敏感性、频域划分性、最优逼近等特性而广受学者关注,被广泛地应用于函数生成、信号图像处理.因此,开展对Shearlet框架的研究不仅具有理论意义而且还具有重要的应用价值.本文的主要工作如下:本文首先对任意正整数尺度因子a(a≥2),构造了一类分段光滑、对称、紧支撑的辅助函数,并讨论了这类辅助函数的有关性质,这为基于辅助函数构造具有良好性质的Parseval Shearlet框架提供条件保障.其次,利用伪极坐标表示、变量替换、频域分割等工具与方法,给出了a进制2维和3维Parseval Shearlet框架的构造方法,此Parseval Shearlet框架是由一个单变量函数生成的.若该单变量函数是无穷次可微的且有限频带的,则所构造的a进制Parseval Shearlet框架元素也是紧支撑无穷次可微的.
[Abstract]:The Shearlet transform generates shear wave functions with different characteristics by scaling, shearing and translation affine transformations to the basis functions, and has the optimal approximation property to the high dimensional signals of singular curves and surfaces. Therefore, the edge information can be captured better, especially for the Shearlet framework, which has the characteristics of multi-resolution analysis, anisotropy, direction-sensitivity, frequency-domain partitioning, optimal approximation and so on. Is widely used in function generation, signal image processing. The main work of this paper is as follows: in this paper, we construct a class of piecewise smooth and symmetric Shearlet frames. The properties of these auxiliary functions are discussed, which provide a conditional guarantee for constructing a Parseval Shearlet framework with good properties based on auxiliary functions. Secondly, the pseudo-polar coordinates are used to replace the variables. In this paper, we give the method of constructing the Parseval Shearlet frame, which is generated by a univariate function, if the univariate function is infinitely differentiable and finite frequency band. The constructed a-ary Parseval Shearlet frame element is also compact-supported infinitely differentiable.
【学位授予单位】：北方民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O174.2

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