A FAMILY OF NONSEPARABLE SMOOTH COMPACTLY SUPPORTED WAVELETS

被引：1
|
作者：
San Antolin, A. [1 ]
Zalik, R. A. [2 ]
机构：
[1] Univ Alicante, Dept Anal Matemat, E-03080 Alicante, Spain
[2] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA
来源：
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING | 2013年 / 11卷 / 02期
关键词：
Fourier transform; multiresolution analysis; nonseparable functions; scaling function; wavelets; CONSTRUCTION; BASES;
D O I：
10.1142/S0219691313500148
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We construct smooth nonseparable compactly supported refinable functions that generate multiresolution analyses on L-2(R-d), d > 1. Using these refinable functions we construct smooth nonseparable compactly supported orthonormal wavelet systems. These systems are nonseparable, in the sense that none of its constituent functions can be expressed as the product of two functions defined on lower dimensions. Both the refinable functions and the wavelets can be made as smooth as desired. Estimates for the supports of these scaling functions and wavelets, are given.
引用
收藏
页数：12
相关论文
共 50 条
  • [1] On the construction of a class of bidimensional nonseparable compactly supported wavelets
    Li, YZ
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (12) : 3505 - 3513
  • [2] Construction of Bivariate Nonseparable Compactly Supported Orthogonal Wavelets
    Leng, Jinsong
    Huang, Tingzhu
    Cattani, Carlo
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2013, 2013
  • [3] Construction of bivariate nonseparable compactly supported biorthogonal wavelets
    Leng, Jin-Song
    Huang, Ting-Zhu
    Fu, Ying-Ding
    [J]. PROCEEDINGS OF 2008 INTERNATIONAL CONFERENCE ON MACHINE LEARNING AND CYBERNETICS, VOLS 1-7, 2008, : 3625 - 3629
  • [4] The construction of a class of trivariate nonseparable compactly supported wavelets
    Huang, Yong-Dong
    Cheng, Zheng-Xing
    [J]. 2007 INTERNATIONAL CONFERENCE ON WAVELET ANALYSIS AND PATTERN RECOGNITION, VOLS 1-4, PROCEEDINGS, 2007, : 1876 - +
  • [5] THE CONSTRUCTION OF A CLASS OF TRIVARIATE NONSEPARABLE COMPACTLY SUPPORTED WAVELETS
    Huang, Yongdong
    Yang, Shouzhi
    Cheng, Zhengxing
    [J]. INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 2009, 7 (03) : 255 - 267
  • [6] PARAMETRIZING SMOOTH COMPACTLY SUPPORTED WAVELETS
    WELLS, RO
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 338 (02) : 919 - 931
  • [7] Examples of bivariate nonseparable compactly supported orthonormal continuous wavelets
    He, WJ
    Lai, MJ
    [J]. IEEE TRANSACTIONS ON IMAGE PROCESSING, 2000, 9 (05) : 949 - 953
  • [8] Examples of bivariate nonseparable continuous compactly supported orthonormal wavelets
    He, WJ
    Lai, MJ
    [J]. WAVELET APPLICATIONS IN SIGNAL AND IMAGE PROCESSING V, 1997, 3169 : 303 - 314
  • [9] A method for constructing trivariate nonseparable compactly supported orthogonal wavelets
    Leng, Jin-Song
    Huang, Ting-Zhu
    Fu, Ying-Ding
    Lai, Choi-Hong
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2009, 86 (07) : 1264 - 1273
  • [10] The construction of a class of trivariate nonseparable compactly supported orthogonal wavelets
    Huang, Yongdong
    Lei, Chongmin
    Yang, Miao
    [J]. CHAOS SOLITONS & FRACTALS, 2009, 40 (03) : 1530 - 1537
12345