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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (1): 11-20.doi: 10.3969/j.issn.1005-3085.2015.01.002

• • 上一篇    下一篇

不可分对称正交小波紧框架的构造

冯  岩1,  沈延峰2,3,  杨守志2,  袁德辉4   

  1. 1- 信阳师范学院计算机与信息技术学院，信阳 464000
    2- 汕头大学数学系，汕头 515063
    3- 德州学院数学科学学院，德州  253023
    4- 韩山师范学院数学与统计学院，韩山 521041
  • 收稿日期:2013-03-14 接受日期:2013-11-28 出版日期:2015-02-15 发布日期:2014-04-15
  • 基金资助:
    国家自然科学基金 (11071152)；河南省自然科学基金 (142300410351)；河南省教育厅科学技术研究重点项目 (14B520045)；广东省自然科学基金 (S2013010013101).

Construction of Nonseparable Orthogonal Wavelet Tight Frames with Symmetry

FENG Yan1,  SHEN Yan-feng2,3,  YANG Shou-zhi2,  YUAN De-hui4   

  1. 1- School of Computer and Information Technology, Xinyang Normal University, Xinyang 464000
    2- Department of Mathematics, Shantou University, Shantou 515063
    3- College of Mathematical Sciences, Dezhou University, Dezhou 253023
    4- Department of Mathematics and statistics, Hanshan Normal University, Hanshan 521041
  • Received:2013-03-14 Accepted:2013-11-28 Online:2015-02-15 Published:2014-04-15
  • Supported by:
    The National Natural Science Foundation of China (11071152); the Natural Science Foundation of Henan Province (142300410351); the Key Basic Foundation of Educational Commission of Henan Province of China (14B520045); the Natural Science Foudation of Guangdong Province (S2013010013101).

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摘要： 与可分小波相比，不可分小波更能捕捉高维信号的高频信息，正交框架在处理高维信号时能避免预滤波．为了更有效地处理高维信号，本文研究了不可分正交小波紧框架的构造，提出了一种由一维小波紧框架来构造高维不可分正交小波紧框架的方法，即先用张量积的方法构造高维小波紧框架，然后乘上一个具有一定性质的三角多项式．如果一维小波紧框架是对称的，用本文提出的方法构造的高维不可分的正交小波紧框架也是对称的．最后给出了一个构造算例．

关键词: 小波紧框架, 正交性, 对称性, 不可分

Abstract:

Nonseparable wavelets can capture high frequency information of multi-dimensional signal compared with separable ones, and orthogonal frames can avoid pre-filtering in processing of multi-dimensional signal. In order to process multi-dimensional signal efficiently, this paper studies the construction of nonseparable orthogonal wavelet tight frames constructed by unidimenstional one through tensor product, and multiplied by a trigonometric polynomial with some properties. Moreover, if the unidimenstional one is symmetric, the one so constructed is also symmetric. Finally, an example is provided.

Key words: wavelet tight frames, orthogonality, symmetry, nonseparable

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