(28) * << * >> * Russian * English * Content * All Issues
The use of canonical number systems in the problem of constructing nonseparable Haar-like wavelets
1Samara State Aerospace University named after academician S.P. Korolev
2Image Processing Systems Institute of RAS
PDF, 118 kB
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.
Haar-like wavelets, Haar-type, wavelet basis, number system, Gaussian integers, quadratic fields.
Belov AM. The use of canonical number systems in the problem of constructing nonseparable Haar-like wavelets. Computer Optics 2005; 28: 119-123.
- Mendivil F, Piché D. Two algorithms for non-separable wavelet transforms and applications to image compression. In Book: Dekking M, Véhel JL, Lutton E, Tricot C, eds. Fractals: Theory and applications in engineering. London Limited: Springer-Verlag; 1999.
- Grochenig K, Madych WR. Multiresolution analysis, Haar bases, and self-similar tilings of Rn. IEEE Trans Inf Theory 1992; 38: 556-568.
- 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.
- Mallat S. Multiresolution analysis and wavelets. Trans Amer Math Soc 1989; 315: 69-88.
- Katai I, Kovacs B. Canonical number systems in imaginary quadratic fields. Acta Math Acad Sci Hungarica 1981; 37: 159-164.
- Katai I, Szabo J. Canonical number systems for complex integers. Acta Sci Math (Szeged) 1975; 37: 255-260.
- Gilbert W. Complex based number systems (Manuscript). Ontario, Canada: University of Waterloo; 2002.
© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: firstname.lastname@example.org ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20