对称-反对称复合伸缩多小波的构造

吴国昌, 田新现, 李登峰

数学学报 ›› 2011, Vol. 54 ›› Issue (5) : 731-738.

PDF(510 KB)
中国科学院数学与系统科学研究院期刊网
PDF(510 KB)
数学学报 ›› 2011, Vol. 54 ›› Issue (5) : 731-738. DOI: 10.12386/A2011sxxb0077
论文

对称-反对称复合伸缩多小波的构造

    吴国昌1, 田新现2, 李登峰3
作者信息 +

The Construction of Symmetric or Antisymmetric Multiwavelets with Composite Dilations

    Guo Chang WU1, Xin Xian TIAN2, Deng Feng LI3
Author information +
文章历史 +

摘要

基于已知的复合伸缩小波, 本文给出一个构造对称反对称复合伸缩多小波的简单方法. 这个方法可增加复合伸缩小波的数量, 而且构造的多小波保持了原来小波的大部分性质.  

Abstract

Based on existing wavelets with composite dilations, we give a way of constructing symmetric or antisymmetric multiwavelets with composite dilations. This way can increase the amount of wavelets with composite dilations. Furthermore, new multiwavelets preserve the most properties of old wavelets.  

关键词

复合伸缩多小波 / 对称性 / Parseval框架

Key words

multiwavelet with composite dilations / symmetric property / parseval frame

引用本文

EndNote

Ris (Procite)

Bibtex

导出引用
吴国昌, 田新现, 李登峰. 对称-反对称复合伸缩多小波的构造. 数学学报, 2011, 54(5): 731-738 https://doi.org/10.12386/A2011sxxb0077
Guo Chang WU, Xin Xian TIAN, Deng Feng LI. The Construction of Symmetric or Antisymmetric Multiwavelets with Composite Dilations. Acta Mathematica Sinica, Chinese Series, 2011, 54(5): 731-738 https://doi.org/10.12386/A2011sxxb0077

参考文献

[1] Daubechies I., Ten Lectures on Wavelets, Philadelphia: SIAM, 1992.

[2] Welland G. V., Beyond Wavelets, San Diego: Academic Press, 2003.

[3] Candès E. J., Donoho D. L., Ridgelets: a key to higher-dimensional intermittency? Philos. Trans. Roy. Soc.London A, 1999, 357(10): 2495-2509.

[4] Coifman R. R., Meyer F. G., Brushlets: A tool for directional image analysis and image compression, Appl.Comput. Harmon. Anal., 1997, 5(1): 147-187.

[5] Candès E. J., Donoho D. L., New tight frames of curvelets and optimal representations of objects with C2singularities, Comm. Pure Appl. Math., 2004, 56(1): 219-266.

[6] Do M. N., Vetterli M., The contourlet transform: An efficient directional multiresolution image representation,IEEE Trans. Image Process., 2005, 14(12): 2091-2106

[7] Guo K., Lim W. Q., Labate D., Weiss G., Wilson E., Wavelets with composite dilations, Electron. Res.Announc. Amer. Math. Soc., 2004, 10(1): 78-87.

[8] Guo K., Labate D., Lim W. Q., Weiss G., Wilson E., Wavelets with composite dilations and their MRAproperties, Appl. Comput. Harmon. Anal., 2006, 20(2): 202-236.

[9] Guo K., Labate D., Optimally Sparse Multidimensional Representation using Shearlets, SIAM J. Math. Anal.,2007, 39(2): 298-318.

[10] Easley G., Labate D., Lim W., Sparse Directional Image Representations using the Discrete Shearlet Transform,Appl. Comput. Harmon. Anal., 2008, 25(1): 25-46.

[11] Kutyniok G., Labate D., Resolution of the Wavefront Set using Continuous Shearlet, Trans. Amer. Math.Soc., 2009, 361(9): 2719-2754.

[12] Easley G. R., Labate D., Colonna F., Shearlet Based Total Variation for Denoising, IEEE Trans. ImageProcess., 2009, 18(2): 260-268.

[13] Yi S., Labate D., Easley G. R., Krim H., A Shearlet Approach to Edge Analysis and Detection, IEEE Trans.Image Process., 2009, 18(5): 929-941.

[14] Krishtal I., Robinson B., Weiss G., Wilson E. N., Some simple Haar-type wavelets in higher dimensions, J.Geom. Anal., 2007, 17(1): 87-96.

[15] Blanchard J. D., Minimally supported frequency composite dilation wavelets, J. Fourier Anal. Appl., 2009,15(6): 796-815.

[16] Blanchard J. D., Minimally supported frequency composite dilation Parseval frame wavelets, J. Geo. Anal.,2009, 19(1): 19-35.

[17] Li D. F., Xue M. Z., Bases and Frames in Banach Spaces, Beijing: Science Press, 2007 (in Chinese).

[18] Li D. F., Yang X. H., Basic Theory of Wavelets and Application Examples, Beijing: Higher Education Press,2010 (in Chinese).

基金

国家自然科学基金资助项目(61071189);河南省创新性科技人才队伍建设工程(084100510012)和省教育厅自然科学基金(2010A110002)

PDF(510 KB)

180

Accesses

0

Citation

Detail
段落导航
相关文章

/

〈 〉