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多进紧支对称小波尺度函数构造及性质 被引量：2

On the Construction and Property of Symmetric Orthogonal Multi-Band Scaling Functions
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摘要 为了克服2进小波的缺陷和拓宽小波的应用,探索了具有任意正则阶正交对称多进小波尺度函数构造的一般方法.讨论了尺度序列与尺度函数性质之间对应关系,得到了正则阶一定条件下最短支集正交对称多进小波尺度函数对应尺度序列构造程序. In order to overcome some of the shortcomings of 2-band wavelet and develop application of wavelet, we provide a general way for constructing symmetric orthogonal multi-band scaling function. The characterizations of scaling function and scaling sequence are considered. A scheme for constructing scaling sequence of shortest length with a given regularity order m is obtained lastly.
作者 全宏跃 王国秋
机构地区 湖南师范大学数学与计算机科学学院 长沙理工大学数学与计算科学学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2009年第4期751-762,共12页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金资助项目(10571049 10871065) 湖南省教育厅自然科学基金资助项目(06A036)
关键词 多进小波 尺度函数 尺度序列 multi-band wavelet scaling function scale sequence
分类号 O174.2 [理学—基础数学]
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参考文献12

  • 1Doubechies I., Orthonormal bases of compactly supported wavelet, Comm. Pure. Appl. Math., 1988, 41: 909-996.
  • 2Doubechies I., Ten Lectures on Wavelet, CBMS-NSF Series in Applied Math., Vol. 61, SIAM, Philadelphia, 1992.
  • 3Steffen P., Heller P., Gopinath R., Burrus C., Theory of regular M-band waveletbases, IEEE Trans. Signal Processing, 1993, 41:3497-3511.
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  • 5Heller P., Rank M wavelets with N vanishing moments, SIAM J. Matrix Anal. Appl., 1995, 16: 502-519.
  • 6Abderrazek K., A family of orthonormal wavelet bases with dilation factor 4, J. Math. Anal. Appl., 2006, 317: 364-379.
  • 7Peng L. Z., Wang Y. G., Algebraic structure and parametrization for orthogonal wavelet of 3-band, Science in China, Series A, 2001, 7(31): 602-614.
  • 8Chui C. K., Lian J. A., Construction of compactly supported symmetric and antisymmetric orthonormal wavelets with scale 3, Appl. Comput. Harmon. Anal., 1996, 2: 21-51.
  • 9Han B., Jia R. Q., Multivaries refinement equations and convergence of subdivision schemes, SIAM J. Math. Anal., 1998, 29:1177-1999.
  • 10Han B., Symmetric orthormal scaling functions and wavelets with dilation factor 4, Adv. Comput. Math., 1998, 8: 221-247.

同被引文献17

  • 1杨守志.紧支撑正交插值的多小波和多尺度函数[J].数学学报（中文版）,2005,48(3):565-572. 被引量：11
  • 2Yun Zhang LI.A Class of Bidimensional FMRA Wavelet Frames[J].Acta Mathematica Sinica,English Series,2006,22(4):1051-1062. 被引量：5
  • 3De Yun YANG,Xing Wei ZHOU,Zhu Zhi YUAN.Frame Wavelets with Compact Supports for L^2(R^n)[J].Acta Mathematica Sinica,English Series,2007,23(2):349-356. 被引量：1
  • 4Doubechies I. Orthonormal bases of compactly supported wavelet [J]. Comm Pure Appl Math,1988, 41:909-996.
  • 5Doubechies I. Ten Lectures on Wavelet [M]. Philadelphia, PA: SIAM, 1992.
  • 6Nguyen T Q, Vaidyanathan P P. Maximally decimated perfect-reconstruction FIR filter banks with pairwise mirror-image analysis and synthesis frequency responses [J]. IEEE Transactions on Acoustics, Speech and Signal , 1998, 36(5):693-706.
  • 7Lian J A. Orthogonality criteria for multi-scaling functions [J]. Appl Comput Harmon Anal, 1998(5):277-311.
  • 8Heller P. Rank M wavelets with N vanishing moments [J]. SIAM Y Matrix Anal Appl, 1995, 16:502-519.
  • 9Abderrazek K. A family of orthonormal wavelet bases with dilation factor 4 [J]. Math Anal Appl, 2006, 317:364-379.
  • 10Chui C K, Lian J A. Construction of compactly supported symmetric and antisymmetric orthonormal wavelets with scale 3 [J]. Appl Comput Harmon Anal, 1996, 2:21-51.

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数学学报（中文版）
2009年 第4期

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