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《Mathematics in Practice and Theory》 2013-17
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On Characterization of Wavelet Phases with MRA in L~2(R~d)

LI Zhong-yan;XU Zhen-yu;Department of Mathematics and Physics,North China Electric Power University;  
Let A be any d×d real expansive matrix,φ be an A-dilation wavelet.A measurable function / is called an A-dilation wavelet multiplier if the inverse Fourier transform of f(ψ)(where(ψ) is the Fourier transform) is an A-dilation wavelet for any A-dilation wavelet φ.In this paper,We mainly characterize the linear phases of A-dilation MRA wavelets in L~2(R~d),where A is expansive matrix with integral entries and |detA|= 2.Using this result,we give the forms of the linear phases of Haar-type and Shannan-type wavelets based on six integrally similar classes of such integral matrices in the two-dimensional case.Finally,we applied the MRA inseparable wavelets with linear phases to the image edge detection in the two-dimensional case.
【Fund】: 国家自然科学基金(11101142);; 中央高校基本科研业务费专项资金资助;; 北京市教委共建项目
【CateGory Index】: O174
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【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 WANG Li-juan,LI Wan-she ,JI ANG Nan(College of Mathematics and Information Science ,Shaanxi Normal University , Xi′an 710062 , China);On the extendability of frame wavelets[J];Basic Sciences Journal of Textile Universities;2008-03
2 LI Wan-she,LI Dong-liang(College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,China);A characterization of A-dilation multi-wavelet set[J];Basic Sciences Journal of Textile Universities;2011-04
3 Sun QiyuDept. of Math.,National University of Singapore,10 Kent Ridge Crescent,Singapore 119260,Singapore.;LINEAR INDEPENDENCE OF THE INTEGER TRANS-LATES OF COMPACTLY SUPPORTED DISTRIBU-TIONS AND REFINABLE VECTORS[J];高校应用数学学报B辑(英文版);2001-04
4 De Yun YANG Department of Information,Taishan University,Taian 271000,P.R.China Department of Automation,Nankai University,Tianjin 300071,P.R.China Xing Wei ZHOU Department of Mathematics and LPMC,Nankai University,Tianjin 300071,P.R.China Zhu Zhi YUAN Department of Automation,Nankai University,Tianjin 300071,P.R.China;Frame Wavelets with Compact Supports for L~2(R~n)[J];数学学报(英文版);2007-02
5 GUO Feng-chen (Department of Mathematics,East China Normal University,Shanghai 200062,China);On the Existence of Wavelets for Non-Expansive Dilation Matrices[J];Journal of East China Normal University(Natural Science);2006-03
6 XIN You-ming ( Department of Mathematics, East China Normal University, Shanghai 200062, China; Department of Mathematics and Physics, Qingdao University of Science and Technology, Shandong Qingdao 266061, China );On the Spectrums of Frame Multiresolution Analysis[J];Journal of East China Normal University(Natural Science);2006-05
7 LI JianLin College of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,China;Analysis of a class of spectral pair conditions[J];中国科学:数学(英文版);2011-10
8 XIN You-ming,CHENG Zun-shui,XING Jian-min(College of Mathematics and Physics,Qingdao University of Science and Technology,Qingdao 266042,China);Existence of FMRA Wavelets for Non-integer Entry Expansive Matrix[J];Journal of Qingdao University of Science and Technology(Natural Science Edition);2009-02
9 LI Wan-she,CHEN Xu-li(College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062,Shaanxi,China);A Characterization of Subspace MRA Wavelets[J];Journal of Shantou University(Natural Science Edition);2011-03
10 LI Wan-she,SHI Hui-ting(College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,China);A NEW METHOD OF CONSTRUCTION OF A-DILATION MRA WAVELETS SETS[J];Journal of Shaanxi University of Science & Technology(Natural Science Edition);2012-01
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