[1]邵云虹,邓彩霞,贺鹏. 利用充分光滑的S形函数构造Meyer小波[J].哈尔滨理工大学学报,2019,(02):127-134.[doi:10.15938/j.jhust.2019.02.019]
 SHAO Yun hong,DENG Cai xia,HE Peng. Construction of Meyer Wavelet Using Fully Smooth Sigmiod Function[J].哈尔滨理工大学学报,2019,(02):127-134.[doi:10.15938/j.jhust.2019.02.019]
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 利用充分光滑的S形函数构造Meyer小波()
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《哈尔滨理工大学学报》[ISSN:1007-2683/CN:23-1404/N]

卷:
期数:
2019年02期
页码:
127-134
栏目:
数理科学
出版日期:
2019-04-25

文章信息/Info

Title:
 Construction of Meyer Wavelet Using Fully Smooth Sigmiod Function
文章编号:
1007-2683(2019)02-0127-08
作者:
 邵云虹邓彩霞贺鹏
 (哈尔滨理工大学 理学院,黑龙江 哈尔滨 150080)
Author(s):
 SHAO YunhongDENG CaixiaHE Peng
 (School of Scinces, Harbin University of Science and Technology, Harbin 150080, China)
关键词:
 小波分析Meyer小波S形函数尺度函数高阶消失矩
Keywords:
 wavelet analysis Meyer wavelet sigmoid function scaling function high order vanishing moment
分类号:
O174.22
DOI:
10.15938/j.jhust.2019.02.019
文献标志码:
A
摘要:
 为了在信号或图像的重构中获得较好的平滑效果,必须尽量增大小波的正则性或者连续可微性。在Meyer小波构造中S形函数的选取影响着Meyer小波的可微性、光滑性和衰减速度等性质,所以S形函数的选取至关重要。给出一种构造充分光滑的S形函数的方法,并以一个充分光滑的非多项式S形函数为例,将其作为BP神经网络中的激励函数进行函数逼近得到好的逼近效果且训练次数少。然后通过充分光滑的S形函数得到Meyer小波的尺度函数,给出相应的具有充分光滑、高阶消失矩且无穷次可微性的频谱有限的Meyer小波。最后把充分光滑的Meyer小波与剪切波变换结合进行图像去噪,与传统的Meyer小波剪切波变换去噪相比较,峰值信噪比高于传统的Meyer剪切波变换且去噪后的图像纹理和边缘信息保留更加完整。
Abstract:
 In order to obtain better smooth effect in signal or image reconstruction, the regularity or continuous differentiability of wavelet must be increased as much as possible The selection of sigmoid function in Meyer wavelet construction affects the differentiability, smoothness and attenuation speed of Meyer wavelet, so it is exceedingly essential to select sigmoid function Firstly, a method of constructing fully smooth sigmoid function is given, and a sufficiently smooth nonpolynomial sigmoid function is taken as an example, which is used as the excitation function in BP neural network for function approximation to obtain good approximation results Then, the scale functions of Meyer wavelets are obtained by fully smooth sigmoid functions Meyer wavelets with limited spectrum are given with sufficient smooth, highorder vanishing moments and infinitesimal differentiability Finally, the full smooth Meyer wavelet and the shearlet transform are combined to denoise the image Compared with the traditional Meyer wavelet shearlet transform, the peak signaltonoise ratio is higher and the denoised image texture and edge information are more complete.

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备注/Memo

备注/Memo:
 收稿日期:2018-09-04
基金项目:国家自然科学基金(11871181)
作者简介:
邓彩霞(1965—),女,博士,教授,硕士研究生导师
通信作者:
邵云虹(1994—),女,硕士研究生,E-mail:18846141926@163.com
更新日期/Last Update: 2019-05-17