<I>r</I>重<I>a</I>尺度正交平衡插值多小波的设计

王刚; 周小辉

doi:10.3724/SP.J.1004.2012.01996

r重a尺度正交平衡插值多小波的设计

doi: 10.3724/SP.J.1004.2012.01996

王刚¹,
周小辉^2,

1.
新疆师范大学数学科学学院乌鲁木齐 830054;
2.
石河子大学理学院数学系石河子 832003

详细信息

通讯作者:
周小辉

计量
- 文章访问数: 1514
- HTML全文浏览量: 37
- PDF下载量: 675
- 被引次数: 0
出版历程
- 收稿日期: 2011-04-08
- 修回日期: 2012-07-25
- 刊出日期: 2012-12-20

The Study of The Orthogonal Balanced Interpolation Multi-wavelets with Multiplicity r and Dilation Factor a

WANG Gang¹,
ZHOU Xiao-Hui^2
,

1.
School of Mathematics Science, Xinjiang Normal University, Urumqi 830054;
2.
Department of Mathematics, Polytechnic Institute of Shihezi University, Shihezi 832003

摘要

摘要: 研究了r重a尺度紧支撑正交平衡插值多小波,其中a≠r.所得的多尺度函数是正交平衡插值的,同时对应的多小波是正交插值的. 首先,根据插值多小波的定义,利用取整函数这一技巧,得到关于r重a尺度插值条件的显式方程.其次,研究了a=2, r=3 和a=2, r=4的紧支撑正交插值多小波,并构造了相应的实例. 最后,利用Gram-Schmidt正交化方法讨论了a=3, r=4的正交插值多小波,并给出了算例.
- 正交多小波 /
- 插值性 /
- 平衡性 /
- 多尺度函数
Abstract: The orthogonal balanced interpolation multi-wavelets with multiplicity r and dilation factor a are discussed in this paper, where a≠r. The obtained multi-scaling function is orthogonal, balanced, and interpolated. And the corresponding multi-wavelets is orthogonal and interpolated. Firstly, according to the definition of interpolation multi-wavelets, the explicit equation of the interpolation condition of the multi-scaling function with multiplicity r and dilation factor a is obtained by using the round-off number function. Secondly, the orthogonal interpolation multi-wavelets with a=2, r=3 and a=2, r=4 are studied, and the corresponding examples are constructed. Finally, the orthogonal interpolation multi-wavelets with a=3, r=4 is constructed by the Gram-Schmidt's orthogonalization and the example is given.
- Orthogonal multi-wavelets /
- interpolation /
- balance /
- multi-scaling function

HTML全文

参考文献(1)

[1]

Yang S Z. Compactly supported orthogonal interpolation multiwavelets and multiscaling functions. Acta Mathematica Sinica, 2005, 48(3): 565-572[2] Li R, Wu G C. The orthogonal interpolating balanced multiwavelet with rational coefficients. Chaos, Solitons and Fractals, 2009, 41(2): 892-899[3] Yang S Z, Wang H Y. High-order balanced multi-wavelets with dilation factor a. Applied Mathematics and Computation, 2006, 181(1): 362-369[4] Yang Shou-Zhi, Peng Li-Zhong. The construction of orthogonal multi-scaling functions with high balance order based on PTST. Science in China Series E: Information Science, 2006, 36(6): 644-656(杨守志, 彭立中. 基于PTST方法构造高阶平衡的正交多尺度函数. 中国科学: E辑信息科学, 2006, 36(6): 644-656)[5] Chen Jun-Li, Jiao Li-Cheng. Design of interpolating orthogonal multiwavelet. Journal of Electronics and Information Technology, 2004, 26(11): 1728-1732(陈俊丽, 焦李成. 正交插值多子波理论和构造. 电子与信息学报, 2004, 26(11): 1728-1732)[6] Lebrun J, Vetterli M. Balanced multiwavelets theory and design. IEEE Transactions on Signal Processing, 1998, 46(4): 1119-1125[7] Lebrun J, Vetterli M. High order balanced multi-wavelets. In: Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing. Seattle, USA: IEEE, 1998. 1529-1532[8] Lian J A, Chui C K. Analysis-ready multiwavelets (armlets) for processing scalar-valued signal. IEEE Signal Processing Letters, 2004, 11(2): 205-208[9] Mao Yi-bo. General cardinal multiwavelets. Journal of Chongqing University (Natural Science Edition), 2007, 30(4): 91-94(毛一波. 广义插值多小波. 重庆大学学报(自然科学版), 2007,30(4): 91-94)[10] Yang Shou-Zhi, Yang Xiao-Zhong. Orthogonal multiscaling functions and multiwavelets with general cardinal property. Acta Mathematica Scientia, 2007, 27(3): 470-475(杨守志, 杨晓忠. 广义基插值的正交多尺度函数和多小波. 数学物理学报, 2007, 27(3): 470-475)[11] Jiang Li, Zhu Shan-Hua, Lv Yong. Balancing of compactly supported interpolatory orthonormal multiwavelets with scale = a. Journal on Numerical Methods and Computer Applications, 2009, 30(1): 10-20(江力, 朱善华, 吕勇. a尺度紧支撑插值正交多小波的平衡性. 数值计算与计算机应用, 2009, 30(1): 10-20)[12] Yang Shou-Zhi, Cao Fei-Long. Orthogonal balanced multi-wavelet with multiplicity r and dilation factor a. Progress in Natural Science, 2005, 16(2): 177-182(杨守志, 曹飞龙. 伸缩因子为a的r重正交平衡的多小波. 自然科学进展, 2005, 16(2): 177-182)[13] Li You-Fa, Yang Shou-Zhi. Construction of paraunitary symmetric matrix and parametrization of symmetric and orthogonal multiwavelets filter banks. Acta Mathematica Sinica, 2010, 53(2): 279-290(李尤发, 杨守志. 仿酉对称矩阵的构造及对称正交多小波滤波带的参数化. 数学学报, 2010, 53(2): 279-290)[14] Cong Xue-Rui, Cui Li-Hong. Construction of interpolatory multiscaling functions with high approximation order. Journal of Beijing University of Chemical Technology (Natural Science Edition), 2008, 35(4): 108-112(丛雪瑞, 崔丽鸿. 具有高逼近阶的插值多尺度函数的构造. 北京化工大学学报(自然科学版), 2008, 35(4): 108-112)[15] Geronimo J S, Hardin D P, Massopust P R. Fractal functions and wavelet expansions based on several scaling functions. Journal of Approximation Theory, 1994, 78(3): 373-401[16] Li Y F, Yang S Z. Explicit construction of symmetric orthogonal wavelet frames in l2(Rs). Journal of Approximation Theory, 2010, 162(5): 891-909[17] Yang Shou-Zhi, Liu Hua-Wei. Construction of M-band orthogonal symmetric interpolatory scaling functions with parameter. Numerical Mathematics——A Journal of Chinese Universities, 2010, 32(2): 173-178(杨守志, 刘华伟. M带含参数对称正交插值尺度函数的构造. 高等学校计算数学学报, 2010, 32(2): 173-178)[18] Xie C Z, Yang S Z. Construction of refinable function vector via GTST. Applied Mathematics and Computation, 2007, 194(2): 425-430[19] Yang S Z, Huang Y D. Construction of a class of compactly supported symmetric and balanced refinable function vector by GTST. Applied Mathematics and Computation, 2009 207(1): 83-89[20] Yang Shou-Zhi, Liu Hua-Wei. Construction of orthogonal symmetric balanced multiscaling functions. Journal of Shantou University (Natural Science Edition), 2010, 22(2): 18-23(杨守志, 刘华伟. 正交对称平衡多尺度函数的构造. 汕头大学学报(自然科学版), 2010, 22(2): 18-23)[21] Li De-Qiang, Wu Yong-Guo, Luo Hai-Bo. Redundant DWT based signal registration and classification. Acta Automatica Sinica, 2011, 37(1): 61-66(李德强, 吴永国, 罗海波. 基于冗余离散小波变换的信号配准及分类. 自动化学报, 2011, 37(1): 61-66)[22] Yang Bo, Jing Zhong-Liang. Image fusion algorithm based on the quincunx-sampled discrete wavelet frame. Acta Automatica Sinica, 2010, 36(1): 12-33(杨波, 敬忠良. 梅花形采样离散小波框架图像融合算法. 自动化学报, 2010, 36(1): 12-33)[23] Wu Xiu-Yong, Xu Ke, Xu Jin-Wu. Automatic recognition method of surface defects based on Gabor wavelet and kernel locality preserving projections. Acta Automatica Sinica, 2010, 36(3): 438-442(吴秀永, 徐科, 徐金梧. 基于Gabor小波和核保局投影算法的表面缺陷自动识别方法. 自动化学报, 2010, 36(3): 438-442)

施引文献

资源附件(0)

访问统计