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2008 | 6 | 1 | 159-169
Tytuł artykułu

On the exact values of coefficients of coiflets

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In 1989, R. Coifman suggested the design of orthonormal wavelet systems with vanishing moments for both scaling and wavelet functions. They were first constructed by I. Daubechies [15, 16], and she named them coiflets. In this paper, we propose a system of necessary conditions which is redundant free and simpler than the known system due to the elimination of some quadratic conditions, thus the construction of coiflets is simplified and enables us to find the exact values of the scaling coefficients of coiflets up to length 8 and two further with length 12. Furthermore for scaling coefficients of coiflets up to length 14 we obtain two quadratic equations, which can be transformed into a polynomial of degree 4 for which there is an algebraic formula to solve them.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
6
Numer
1
Strony
159-169
Opis fizyczny
Daty
wydano
2008-03-01
online
2008-02-26
Twórcy
autor
autor
Bibliografia
  • [1] Adams W.W., Loustaunau P., An Introduction to Gröbner Bases, American Mathematical Society, 1994
  • [2] Antonini M., Barlaud M., Mathieu P., Daubechies I., Image coding using wavelet transforms, IEEE Trans. Image Process., 1992, 1, 205–220 http://dx.doi.org/10.1109/83.136597
  • [3] Beylkin G., On the representation of operators in bases of compactly supported wavelets, SIAM J. Numer. Anal., 1992, 29, 1716–1740 http://dx.doi.org/10.1137/0729097
  • [4] Beylkin G., Coifman R.R., Rokhlin V., Fast wavelet transforms and numerical algorithms I, Comm. Pure Appl. Math., 1991, 44, 141–183 http://dx.doi.org/10.1002/cpa.3160440202
  • [5] Bittner K., Urban K., Adaptive wavelet methods using semiorthogonal spline wavelets: Sparse evaluation of nonlinear functions, preprint
  • [6] Buchberger B., An algorithm for finding a basis for the residue class ring of a zero-dimensional polynomial ideal, PhD thesis, University of Inssbruck, Austria, 1965 (in German)
  • [7] Burrus C.S., Odegard J.E., Coiflet Systems and Zero Moments, IEEE Trans. Signal Process., 1998, 46, 761–766 http://dx.doi.org/10.1109/78.661342
  • [8] Burrus C.S., Gopinath R.A., On the moments of the scaling function ψ 0, Proceedings of the ISCAS-92, 1992, 963–966
  • [9] Černá D., Finěk V., On the computation of scaling coefficients of Daubechies wavelets, Cent. Eur. J. Math., 2004, 2, 399–419 http://dx.doi.org/10.2478/BF02475237
  • [10] Chyzak F., Paule P., Scherzer O., Schoisswohl A., Zimmermann B., The construction of orthonormal wavelets using symbolic methods and a matrix analytical approach for wavelets on the interval, Experiment. Math., 2001, 10, 67–86
  • [11] Cohen A., Ondelettes analyses multirésolutions et filtres miroir en quadrature, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1990, 7, 439–459
  • [12] Cohen A., Daubechies I., Feauveau J.C., Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., 1992, 45, 485–500 http://dx.doi.org/10.1002/cpa.3160450502
  • [13] Dahmen W., Kunoth A., Urban K., Biorthogonal spline wavelets on the interval - stability and moment conditions, Appl. Comput. Harmon. Anal., 1999, 6, 132–196 http://dx.doi.org/10.1006/acha.1998.0247
  • [14] Daubechies I., Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math., 1988, 41, 909–996 http://dx.doi.org/10.1002/cpa.3160410705
  • [15] Daubechies I., Orthonormal bases of compactly supported wavelets II Variations on a theme, SIAM J. Math. Anal., 1993, 24, 499–519 http://dx.doi.org/10.1137/0524031
  • [16] Daubechies I., Ten lectures on wavelets, SIAM, Philadelphia, 1992
  • [17] Eirola T., Sobolev characterization of compactly supported wavelets, SIAM J. Math. Anal., 1992, 23, 1015–1030 http://dx.doi.org/10.1137/0523058
  • [18] Finěk V., Approximation properties of wavelets and relations among scaling moments, Numer. Funct. Anal. Optim., 2004, 25, 503–513 http://dx.doi.org/10.1081/NFA-200041709
  • [19] Finěk V., Approximation properties of wavelets and relations among scaling moments II, Cent. Eur. J. Math., 2004, 2, 605–613 http://dx.doi.org/10.2478/BF02475967
  • [20] Lawton W.M., Necessary and sufficient conditions for constructing orthonormal wavelet bases, J. Math. Phys., 1991, 32, 57–61 http://dx.doi.org/10.1063/1.529093
  • [21] Lebrun J., Selesnick I., Grobner bases and wavelet design, J. Symb. Comp., 2004, 37, 227–259 http://dx.doi.org/10.1016/j.jsc.2002.06.002
  • [22] Monzón L., Beylkin G., Hereman W., Compactly supported wavelets based on almost interpolating and nearly linear phase filters (coiflets), Appl. Comput. Harmon. Anal., 1999, 7, 184–210 http://dx.doi.org/10.1006/acha.1999.0266
  • [23] Regensburger G., Scherzer O., Symbolic computation for moments and filter coefficients of scaling functions, Ann. Comb., 2005, 9, 223–243 http://dx.doi.org/10.1007/s00026-005-0253-7
  • [24] Regensburger G., Parametrizing compactly supported orthonormal wavelets by discrete moments, Applicable Algebra in Engineering, Communication and Computing, 2007, 18, 583–601 http://dx.doi.org/10.1007/s00200-007-0054-9
  • [25] Resnikoff H.L., Wells R.O., Wavelet analysis. The scalable structure of information, Springer-Verlag, New York, 1998
  • [26] Shann W.C., Yen C.C., On the exact values of orthonormal scaling coefficients of length 8 and 10, Appl. Comput. Harmon. Anal., 1999, 6, 109–112 http://dx.doi.org/10.1006/acha.1997.0240
  • [27] Tian J., The mathematical theory and applications of biorthogonal Coifman wavelet systems, Ph.D. thesis, Rice University, Houston, TX, 1996
  • [28] Tian J., Wells R.O. Jr., Vanishing moments and biorthogonal Coifman wavelet systems, Proceedings of 4th International Conference on Mathematics in Signal Processing, University of Warwick, England, 1997
  • [29] Tian J., Wells R.O. Jr., Vanishing moments and wavelet approximation, Technical Report, CML TR95-01, Rice University, January 1995
  • [30] Unser M., Approximation power of biorthogonal wavelet expansions, IEEE Transactions on Signal Processing, 1996, 44, 519–527 http://dx.doi.org/10.1109/78.489025
  • [31] Villemoes L.F., Energy moments in time and frequency for two-scale difference equation solutions and wavelets, SIAM J. Math. Anal., 1992, 23, 1519–1543 http://dx.doi.org/10.1137/0523085
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-008-0011-2
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