本文選題：輔助函數(shù)　切入點(diǎn)：a進(jìn)制　出處：《北方民族大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：Shearlet變換通過對(duì)基函數(shù)縮放、剪切和平移仿射變換生成具有不同特征的剪切波函數(shù),對(duì)奇異曲線和曲面的高維信號(hào)具有最優(yōu)逼近特性,故可以更好地捕捉圖像邊緣信息.特別是Shearlet框架,由于同時(shí)具有多分辨分析、各向異性、方向敏感性、頻域劃分性、最優(yōu)逼近等特性而廣受學(xué)者關(guān)注,被廣泛地應(yīng)用于函數(shù)生成、信號(hào)圖像處理.因此,開展對(duì)Shearlet框架的研究不僅具有理論意義而且還具有重要的應(yīng)用價(jià)值.本文的主要工作如下:本文首先對(duì)任意正整數(shù)尺度因子a(a≥2),構(gòu)造了一類分段光滑、對(duì)稱、緊支撐的輔助函數(shù),并討論了這類輔助函數(shù)的有關(guān)性質(zhì),這為基于輔助函數(shù)構(gòu)造具有良好性質(zhì)的Parseval Shearlet框架提供條件保障.其次,利用偽極坐標(biāo)表示、變量替換、頻域分割等工具與方法,給出了a進(jìn)制2維和3維Parseval Shearlet框架的構(gòu)造方法,此Parseval Shearlet框架是由一個(gè)單變量函數(shù)生成的.若該單變量函數(shù)是無窮次可微的且有限頻帶的,則所構(gòu)造的a進(jìn)制Parseval Shearlet框架元素也是緊支撐無窮次可微的.
[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.
【學(xué)位授予單位】：北方民族大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O174.2

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本文編號(hào)：1652275