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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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Chinese Journal Full-text Database 10 Hits
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