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Wavelets and Wavelet Packets Related to a Class of Dilation Matrices

Wavelets and Wavelet Packets Related to a Class of Dilation Matrices
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摘要 The construction of wavelets generated from an orthogonal multiresolution analysis can be reduced to the unitary extension of a matrix,which is not easy in most cases.Jia and Micchelli gave a solution to the problem in the case where the dilation matrix is 21 and the dimension does not exceed 3.In this paper,by the method of unitary extension of a matrix,we obtain the construction of wavelets and wavelet packets related to a class of dilation matrices. The construction of wavelets generated from an orthogonal multiresolution analysis can be reduced to the unitary extension of a matrix,which is not easy in most cases.Jia and Micchelli gave a solution to the problem in the case where the dilation matrix is 21 and the dimension does not exceed 3.In this paper,by the method of unitary extension of a matrix,we obtain the construction of wavelets and wavelet packets related to a class of dilation matrices.
作者 QiaoFangLIAN
机构地区 DepartmentofMathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第5期879-892,共14页 数学学报（英文版）
基金 Supported by the National Natural Science Foundation of China,the Morningside Center of Mathematics of the Chinese Academy of Sciences the Program of"One Hundred Distinguished Chinese Scientists"of the Chinese Academy of Sciences partially supporte by the graduate innovation foundation
关键词 Multiresolution analysis Full set WAVELET Wavelet packet Multiresolution analysis Full set Wavelet Wavelet packet
分类号 O212.5 [理学—概率论与数理统计]
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参考文献9

  • 1Mallat, S. G.: Multiresolution approximations and wavelet orthonormal basis of L2(R). Trans. Amer.Math. Soc., 315, 69-87 (1989).
  • 2Meyer, Y.: Ondelettes et fonctions splines, Seminaire Equations aux Derinees Partielles, Ecole Polytechnique, Paris, France, 1986.
  • 3Daubechies, I.: Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math., 41,909-996 (1988).
  • 4Micchelli, C. A.: Using the refinable equation for the construction of pre-wavelets. Numerical Algorithms,1, 75-116 (1991).
  • 5Micchelli, C. A. and Xu, Y.: Reconstruction and decomposition algorithms for biorthogonal multiwavelets.Multidimensional Systems and Signal Processing, 8, 31 19 (1997).
  • 6Cohen, A., Dahmen, W. and DeVore, R.: Multiscale decompositions on bounded domains. Trans. Amer.Math. Soc., 352, 3651-3685 (2000).
  • 7Jia, R. Q. and Micchelli, C. A.: Using the refinement equations for the construction of pre-wavelets II:powers of two. in Curves and Surfaces, Laurent P. J., Le Mehaute A., and Schumaker L. L., eds., Academic Press, New York, 209 246, 1991.
  • 8Belogay, E., Wang, Y.: Arbitrarily smooth orthogonal nonseparable wavelets in R2. SIAM J. Math. Anal.,30, 678-697 (1999).
  • 9Cohen, A., Daubechies, I.: Non-separable bidimensional wavelet bases. Rev. Mat. Iberoamericana, 9,51-137 (1993).
Acta Mathematica Sinica,English Series
2004年 第5期

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