CONSTRUCTION OF MRA E-TIGHT FRAME WAVELETS, MULTIPLIERS AND CONNECTIVITY PROPERTIES

Author(s):  
DENG-FENG LI ◽  
JUN-FANG CHENG

A method that constructs an MRA E-tight frame wavelet by using a generalized low pass E-filter is given, and it is showed that all of MRA E-tight frame wavelets can be obtained via the method, where the dilation matrix E is the quincunx matrix or the matrix consists of (0, 1)T and (2, 0)T. Furthermore, the properties of MRA E-tight frame wavelet multipliers as well as E-pseudoscaling function multipliers and generalized low pass E-filter multipliers are characterized. In addition, as an application of these multipliers, we discuss the connectivity of the set of all MRA E-tight frame wavelets in L2(R2).

2010 ◽  
Vol 2010 ◽  
pp. 1-26 ◽  
Author(s):  
Huang Yongdong ◽  
Zhu Fengjuan

We study all generalized low-pass filters and tight frame wavelets with special dilation matrixM(M-TFW), whereMsatisfiesMd=2Idand generates the checkerboard lattice. Firstly, we study the pseudoscaling function, generalized low-pass filters and multiresolution analysis tight frame wavelets with dilation matrixM(MRA M-TFW), and also give some important characterizations about them. Then, we characterize all M-TFW by showing precisely their corresponding dimension functions which are nonnegative integer valued. Finally, we also show that an M-TFW arises from our MRA construction if and only if the dimension of a particular linear space is either zero or one.


Author(s):  
D. E. Luzzi ◽  
L. D. Marks ◽  
M. I. Buckett

As the HREM becomes increasingly used for the study of dynamic localized phenomena, the development of techniques to recover the desired information from a real image is important. Often, the important features are not strongly scattering in comparison to the matrix material in addition to being masked by statistical and amorphous noise. The desired information will usually involve the accurate knowledge of the position and intensity of the contrast. In order to decipher the desired information from a complex image, cross-correlation (xcf) techniques can be utilized. Unlike other image processing methods which rely on data massaging (e.g. high/low pass filtering or Fourier filtering), the cross-correlation method is a rigorous data reduction technique with no a priori assumptions.We have examined basic cross-correlation procedures using images of discrete gaussian peaks and have developed an iterative procedure to greatly enhance the capabilities of these techniques when the contrast from the peaks overlap.


2003 ◽  
Vol 38 (1) ◽  
pp. 75-98 ◽  
Author(s):  
Gustavo Garrigos
Keyword(s):  

2008 ◽  
Vol 107 (1-3) ◽  
pp. 195-201 ◽  
Author(s):  
Marcin Bownik
Keyword(s):  

2001 ◽  
Vol 11 (2) ◽  
pp. 311-342 ◽  
Author(s):  
Maciej Paluszyński ◽  
Hrvoje Šikić ◽  
Guido Weiss ◽  
Shaoliang Xiao

2013 ◽  
Vol 712-715 ◽  
pp. 2458-2463
Author(s):  
Qing Jiang Chen ◽  
Xiao Ting Lei ◽  
Jian Feng Zhou

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this paper, we discuss a new set of symmetric tight frame wave-lets with the associated filterbanks outputs downsampled by several generators. The frames consist of several generators obtained from the lowpass filter using spectral factorization, with lowpass fil-ter via a simple approach using Legendre polynomials. The filters are feasible to be designed and offer smooth scaling functions and frame wavelets. We shall give an example to demonstrste that so -me examples of symmetric tight wavelet frames with three compactly supported real-valued sym- metric generators will be presented to illustrate the results.


2005 ◽  
Vol 53 (1) ◽  
pp. 231-239 ◽  
Author(s):  
A.F. Abdelnour ◽  
I.W. Selesnick
Keyword(s):  

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