The Phase Of Wavelets In High-dimensional And Its Application

Let A be any d×d real expansive matrix,ψ be an A-dilation wavelet, ψ be its Fourier transform. A measurable function f is called an A-dilation wavelet multiplier if the inverse Fourier transform of fψ is an A-dilation wavelet for any A-dilation wavelet y/. In this paper, we mainly characterize the linear phases of A-dilation MRA wavelet in L2(Rd), where A is expansive matrices with integral entries and|det(A)|=2. Using this result, we give the forms of the linear phases of Haar-type and Shannon-type wavelets under high-dimensional case, and obtaine the linear phases based on six integrally similar classes of such integral matrices in the two-dimensional case. Finally, we applied the MRA inseparable wavelet with linear phase to the image edge detection in the two-dimensional case.