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2008 | 6 | 4 | 504-525
Tytuł artykułu

A general construction of nonseparable multivariate orthonormal wavelet bases

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The construction of nonseparable and compactly supported orthonormal wavelet bases of L 2(R n); n ≥ 2, is still a challenging and an open research problem. In this paper, we provide a special method for the construction of such wavelet bases. The wavelets constructed by this method are dyadic wavelets. Also, we show that our proposed method can be adapted for an eventual construction of multidimensional orthogonal multiwavelet matrix masks, candidates for generating multidimensional multiwavelet bases.
Wydawca
Czasopismo
Rocznik
Tom
6
Numer
4
Strony
504-525
Opis fizyczny
Daty
wydano
2008-12-01
online
2008-10-08
Twórcy
Bibliografia
  • [1] Cohen A., Daubechies I., Non-separable bidimensional wavelet bases, Rev. Mat. Iberoamericana, 1993, 9, 51–137 http://dx.doi.org/10.1146/annurev.ms.09.080179.000411
  • [2] Daubechies I., Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, 61, SIAM, Philadelphia, PA, 1992
  • [3] Ji H., Riemenschneider S.D., Shen Z., Multivariate compactly supported fundamental refinable functions, duals, and biorthogonal wavelets, Stud. Appl. Math., 1999, 102, 173–204 http://dx.doi.org/10.1111/1467-9590.00108
  • [4] Karoui A., A technique for the construction of compactly supported biorthogonal wavelets of L 2(Rn); n ≥ 2, J. Math. Anal. Appl., 2000, 249, 367–392 http://dx.doi.org/10.1006/jmaa.2000.6867
  • [5] Karoui A., A note on the construction of nonseparable wavelet bases and multiwavelet matrix filters of L 2(R n); where n ≥ 2, Electron. Res. Announc. Amer. Math. Soc., 2003, 9, 32-39
  • [6] Kovačević J., Vetterli M., Nonseparable two-and three-dimensional wavelets, IEEE Trans. Signal Process., 1995, 43, 1269–1273 http://dx.doi.org/10.1109/78.382414
  • [7] Lai M.-J., Methods for Constructing Nonseparable Wavelets, In: Wavelet Analysis: twenty year’s development, D.X. Zhou (Ed.), World Scientific, 2002, 231–251
  • [8] Lawton W., Lee S.L., Shen Z., Stability and orthonormality of multivariate refinable functions, SIAM J. Math. Anal., 1997, 28, 999–1014 http://dx.doi.org/10.1137/S003614109528815X
  • [9] Lin E.B., Ling Y., Image compression and denoising via nonseparable wavelet approximation, J. Comput. Appl. Math., 2003, 155, 131–152 http://dx.doi.org/10.1016/S0377-0427(02)00896-8
  • [10] Maass P., Families of orthogonal two-dimensional wavelets, SIAM J. Math. Anal., 1996, 27, 1454–1481 http://dx.doi.org/10.1137/S003614109324649X
  • [11] Shen Z., Refinable function vectors, SIAM J. Math. Anal., 1998, 29, 235–250 http://dx.doi.org/10.1137/S0036141096302688
  • [12] Wang J.W., Chen C.H., Chien W.M., Tsai C.M., Texture classification using non-separable two-dimensional wavelets, Pattern Recognition Letters, 1998, 19, 1225–1234 http://dx.doi.org/10.1016/S0167-8655(98)00105-6
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0052-6
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