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The use of canonical number systems in the problem of constructing nonseparable Haar-like wavelets

A.M. Belov1,2
1Samara State Aerospace University named after academician S.P. Korolev 

2Image Processing Systems Institute of RAS 


 PDF, 118 kB

Pages: 119-123.

Abstract:
The paper generalizes the method of constructing a Haar-like orthonormal wavelet basis over L2(Rn) based on the characteristic functions of fundamental domains of number systems. In the prototype work, the construction of a Haar-like wavelet basis was based on the existence of a positional number system in the ring of Gaussian integers. In this paper, the authors consider the construction of a Haar-like wavelet basis over L2(R2) associated with canonical number systems in other quadratic fields.

Keywords:
Haar-like wavelets, Haar-type, wavelet basis, number system, Gaussian integers, quadratic fields.

Citation:
Belov AM. The use of canonical number systems in the problem of constructing nonseparable Haar-like wavelets. Computer Optics 2005; 28: 119-123.

References:
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  2. Grochenig K, Madych WR. Multiresolution analysis, Haar bases, and self-similar tilings of Rn. IEEE Trans Inf Theory 1992; 38: 556-568. 
  3. Piché DG. Complex bases, number systems and their application to fractal-wavelet image coding. PhD in Applied Mathematics thesis. Ontario, Canada: University of Waterloo; 2002. 
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  5. Katai I, Kovacs B. Canonical number systems in imaginary quadratic fields. Acta Math Acad Sci Hungarica 1981; 37: 159-164. 
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