Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1
Chinese Journal of Engineering Mathematics

Chinese Journal of Engineering Mathematics ›› 2015, Vol. 32 ›› Issue (1): 11-20.doi: 10.3969/j.issn.1005-3085.2015.01.002

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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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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

CLC Number: