a尺度二维四向双正交多小波的构造和Mallat算法
The Construction and the Mallat Algorithm of Biorthogonal Two Dimensional Four-Direction Multi-Wavelet with Dilation Factor a
摘要:
通过二维四向多加细函数以及二维四向多小波的概念，推广二尺度二维四向正交多小波为a尺度二维四向双正交多小波，更进一步对于a尺度二维四向双正交多加细函数和多小波的构造算法做出了相应给出，最后研究了a尺度二维四向多小波的Mallat算法。
Abstract:
Through the concept of two dimensional four-direction multi-scaling function and two dimensional four-direction multi-wavelet, the two dimensional four-direction orthogonal multi-wavelet with dilation factor two is generalized to two dimensional biorthogonal multi-wavelet with dilation factor a. Furthermore, the construction algorithm of two dimensional biorthogonal multi-scaling function and multi-wavelet with dilation factor a is given. Finally, the Mallat algorithm of two dimensional four-direction multi-wavelet with dilation factor a is studied.
参考文献
|
[1]
|
杨守志, 李尤发. 具有高阶逼近阶和正则性的双正交加细函数和双向小波[J]. 中国科学A辑: 数学, 2007, 37(7): 779-795.
|
|
[2]
|
库福立, 王刚, 库媛. a尺度的二维四向小波问题[J]. 吉林大学学报: 理学版, 2013, 51(5): 763-782.
|
|
[3]
|
李万社, 郝伟, 蒙少亭. a尺度正交双向小波的Mallat算法[J]. 陕西师范大学学报: 自然科学, 2010, 38(3): 1-5.
|
|
[4]
|
陈江清, 程正兴, 杨守志. 向量值正交小波包[J]. 应用数学, 2005, 18(4): 505-515.
|
|
[5]
|
Yang, S.Z. (2006) Biorthogonal Two-Direction Refinable Function and Two Direction Wavelet. Applied Math and Computation, 182, 1717-1724. [Google Scholar] [CrossRef]
|
|
[6]
|
Yang, S.Z. and Li, Y.F. (2007) Two-Direction Refinable Function and Two-Direction Wavelet with Dilation Factor m. Applied Math and Computation, 188, 1908-1920. [Google Scholar] [CrossRef]
|
|
[7]
|
Xie, C.Z. (2008) Constrution of Biorthogonal Two-Direction Refinable Function and Two-Direction Wavelet with Dilation Factor m. Computers and Methematics with Application, 56, 1845-1851. [Google Scholar] [CrossRef]
|
|
[8]
|
杨守志, 程正兴. a尺度多重正交小波包[J]. 应用数学, 2000, 13(1): 61-65.
|
|
[9]
|
Yang, S.Z. and Xue, Y.M. (2009) Two-Direction Poly-Scale Refinability. Computers and Methematics with Application, 58, 119-127. [Google Scholar] [CrossRef]
|