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Some generalized method for constructing nonseparable compactly supported wavelets in L2(R2)

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Języki publikacji
EN
Abstrakty
EN
In this paper we show the construction of nonseparable compactly supported bi-variate wavelets. We deal with the dilation matrix [formula] and some three-row coefficient mask; that is a scaling function that satisfies a dilation equation with scaling coefficients which can be contained in the set {cn} n ∈ s where S = S1 x {0, 1, 2}, S1 ⊂ N, #S1 < ∞
Rocznik
Strony
223--235
Opis fizyczny
Bibliogr. 17 poz., rys.
Twórcy
autor
  • AGH University of Science and Technology Faculty of Applied Mathematics al. A. Mickiewicza 30, 30-059 Krakow, Poland
Bibliografia
  • [1] A. Ayache, Construction of nonseparable dyadic compactly supported orthonormal wavelet bases for L2(R2) of arbitrarily high regularity, Rev. Mat. Iberoamericana 15 (1999), 37-58.
  • [2] A. Ayache, Some methods for constructing nonseparable, orthonormal, compactly supported wavelet bases, Appl. Comput. Harmon. Anal. 10 (2001), 99-111.
  • [3] E. Belogay, Y. Wang, Arbitrarily smooth orthogonal nonseparable wavelets in R2, SIAM J. Math. Anal. 30 (1999), 678-697.
  • [4] M. Bownik, Tight frames of multidimensional wavelets, J. Fourier Anal. Appl. 3 (1997), 525-542.
  • [5] Q.-J. Chen, X.-G. Qu, Characteristics of a class of vector-valued non-separable higher-dimensional wavelet packet bases, Chaos Solitons Fractals 41 (2009) 4, 1676-1683.
  • [6] A. Cohen, I. Daubechies, Nonseparable bidimensional wavelet bases, Rev. Mat. Iberoamericana 9 (1993), 51-137.
  • [7] I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988), 909-996.
  • [8] I. Daubechies, Ten Lectures on Wavelets, Society for Industrial and Applied Math., Philadelphia 1992.[9] K. Gröchenig, W. Madych, Multiresolution analysis, Haar bases, and self-similar tilings, IEEE Trans. Inform. Theory 38 (1992), 558-568.
  • [10] J. Kovačević, M.A. Vetterli, Nonseparable two- and three- dimensional wavelets, IEEE Trans. Signal Process. 43 (1995) 5, 1269-1272.
  • [11] J. Lagarias, Y. Wang, Orthogonality criteria for compactly supported refinable functions and refinable function vectors, J. Fourier Anal. Appl. 6 (2000) 2, 153-170.
  • [12] B. Liu, J. Peng, Multi-spectral image fusion method based on two channels non-separable wavelets, Sci. China Ser. F. 51 (2008) 12, 2022-2032.
  • [13] W.R. Madych, Some elementary properties of multiresolution analyses of L2(Rn), [in:] A Tutorial in Theory and Applications, C.K. Chui, ed., Academic Press, 1992, 259-277.
  • [14] S. Mallat, Multiresolution analysis and wavelets, Trans. Amer. Math. Soc. 315 (1989), 69-88.
  • [15] C.-Y. Wang, Z.-X. Hou, A.-P. Yang, Binary tree image coding algorithm based on non-separable wavelet transform via lifting scheme, Int. J. Wavelets Multiresolut. Inf. Process. 6 (2008) 5, 761-775.
  • [16] P. Wojtaszczyk, Teoria falek [Wavelets Theory], PWN, Warszawa, 2000 [in Polish].
  • [17] J. Zhang, A comparative study of non-separable wavelet and tensor-product wavelet in image compression, CMES Comput. Model. Eng. Sci. 22 (2007) 2, 91-96.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7b2f4dd5-a768-458a-9bc5-150911298d8a
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