多重a尺度双向双正交向量值小波的构造
|
摘要
基于双向向量值小波的基本理论,通过酉矩阵,给出了a尺度r重双向向量值小波双正交条件,得到了a尺度r重双向向量值构造算法,最后给出算例.
Based on the basic theory of vector-valued wavelet, through a unitary matrix, a Two-diection vector-valued bi-orthogonal Multiwavelet are given,he Construction of biorthogonal Two-direction vector-valued MultiwaveletWas obtained,An examples is given.
Based on the basic theory of vector-valued wavelet, through a unitary matrix, a Two-diection vector-valued bi-orthogonal Multiwavelet are given,he Construction of biorthogonal Two-direction vector-valued MultiwaveletWas obtained,An examples is given.
引文
[1]XG Xia, BWSuter. Vector-valued wavelets and vector filter banks[J]. Signal Processing, IEEE Transactions on, 1996, 44(3):508-518.
[2]Coif Man R R, Meyer Y, Wickerhau Ser M V. Their Application[M]. Baston Jones and Bartlet,MA, 1992:145-150.
[3]Bacchelli S, Papi S. Matrix thresholding for multiwavelet image denoising[J]. Numerical Algorithms,2003, 33(1-4):41-52.
[4]Chen Q J, Chen H, Gao H W. The characterization of two-direction vector-valued wavelets and its applications in material engineering[J]. Applied Mechanics and Materials, 2014, 457:36-39.
[5]Yang Shouzhi, Cheng Zhengxing, Wang Hongyong. Construction of biorthogonal multiwavelets[J].Mathematical analysis and Applications, 2002, 276:1-12.
[6]Chen Q J, Cheng Z X, Wang C L. Existence and construction of compactly supported biorthogonal multiple vector-valued wavelets[J]. Journal of Applied Mathematics and Computing, 2006, 22(3):101-115.
[7]Chen Q J, Cheng Z. A study on compactly supported orthogonal vector-valued wavelets and wavelet packets[J]. Chaos, Solitons&Fractals, 2007, 31(4):1024-1034.
[8]Chen Q J, Shi Z. Biorthogonal multiple vector-valued multivariate wavelet packets associated with a dilation matrix[J]. Chaos, Solitons&Fractals, 2008, 35(2):323-332.
[9]陈清江,王满.矩阵伸缩的多元多重向量值小波包的双正交性[J].高等学校计算数学学报,2009, 31(3):267-276.
[10]Chen Q J, Qu X G. Characteristics of a class of vector-valued non-separable higher-dimensional wavelet packet bases[J]. Chaos, Solitons&Fractals, 2009, 41(4):1676-1683.
[11]Lisuo Luo, Wanshe Li, Qiao Li. A study on orthogonal two-direction vector-vallued wavelets and two-direction wavelet packets[J]. Applied Mathematics and Computation, 2011, 21(2):10146-10157.
[12]杨守志,李尤发.具有高逼近阶和正则性的双向加细函数和双向小波[J].中国科学A辑:数学,2007,37(2):770-795.
[13]Yang S Z, Xie C Z. A class of orthogonal two-direction refinable functions and two-direction wavelets[J]. International Journal of Wavelets, Multiresolution and Information Processing, 2008,6(06):883-894.
[14]陈清江,王晓凤,白娜等.多尺度双向向量值小波的构造与性质[J].应用数学,2015, 28(3):662-673.
[15]李岚,陈清江,李娜.伸缩因子为正整数A的双向双正交小波包.[J].工程学报,2010(1):902-910.
[16]Cen Yigang, Cen Lihui. Explicit construction of high-pass filter sequence for orthogonal multiwavelets[J]. Appled Mathematics and Computation, 2009, 3(11):1-14.
[2]Coif Man R R, Meyer Y, Wickerhau Ser M V. Their Application[M]. Baston Jones and Bartlet,MA, 1992:145-150.
[3]Bacchelli S, Papi S. Matrix thresholding for multiwavelet image denoising[J]. Numerical Algorithms,2003, 33(1-4):41-52.
[4]Chen Q J, Chen H, Gao H W. The characterization of two-direction vector-valued wavelets and its applications in material engineering[J]. Applied Mechanics and Materials, 2014, 457:36-39.
[5]Yang Shouzhi, Cheng Zhengxing, Wang Hongyong. Construction of biorthogonal multiwavelets[J].Mathematical analysis and Applications, 2002, 276:1-12.
[6]Chen Q J, Cheng Z X, Wang C L. Existence and construction of compactly supported biorthogonal multiple vector-valued wavelets[J]. Journal of Applied Mathematics and Computing, 2006, 22(3):101-115.
[7]Chen Q J, Cheng Z. A study on compactly supported orthogonal vector-valued wavelets and wavelet packets[J]. Chaos, Solitons&Fractals, 2007, 31(4):1024-1034.
[8]Chen Q J, Shi Z. Biorthogonal multiple vector-valued multivariate wavelet packets associated with a dilation matrix[J]. Chaos, Solitons&Fractals, 2008, 35(2):323-332.
[9]陈清江,王满.矩阵伸缩的多元多重向量值小波包的双正交性[J].高等学校计算数学学报,2009, 31(3):267-276.
[10]Chen Q J, Qu X G. Characteristics of a class of vector-valued non-separable higher-dimensional wavelet packet bases[J]. Chaos, Solitons&Fractals, 2009, 41(4):1676-1683.
[11]Lisuo Luo, Wanshe Li, Qiao Li. A study on orthogonal two-direction vector-vallued wavelets and two-direction wavelet packets[J]. Applied Mathematics and Computation, 2011, 21(2):10146-10157.
[12]杨守志,李尤发.具有高逼近阶和正则性的双向加细函数和双向小波[J].中国科学A辑:数学,2007,37(2):770-795.
[13]Yang S Z, Xie C Z. A class of orthogonal two-direction refinable functions and two-direction wavelets[J]. International Journal of Wavelets, Multiresolution and Information Processing, 2008,6(06):883-894.
[14]陈清江,王晓凤,白娜等.多尺度双向向量值小波的构造与性质[J].应用数学,2015, 28(3):662-673.
[15]李岚,陈清江,李娜.伸缩因子为正整数A的双向双正交小波包.[J].工程学报,2010(1):902-910.
[16]Cen Yigang, Cen Lihui. Explicit construction of high-pass filter sequence for orthogonal multiwavelets[J]. Appled Mathematics and Computation, 2009, 3(11):1-14.