研究多重向量值双正交小波的存在性及构造问题.在给定一对多重向量值双正交尺度函数的情形下,运用向量细分格和矩阵理论,证明与之对应的一对多重向量值双正交小波的存在性.给出一类紧支撑多重向量值双正交小波的构造算法.
[1] 张钦礼, 张翠莲, 曾大有, 赵燕, ZHANG Qin-li, ZHANG Cui-lian, ZENG Da-you, ZHAO Yan. 具有奇偶性的多尺度小波 [J]. 河北大学学报(自然科学版) 2005.doi:10.3969/j.issn.1000-1565.2005.02.002
[2] 陈清江, 李淑玲, 李学志, 程正兴, CHEN Qing-jiang, LI Shu-ling, LI Xue-zhi, CHENG Zheng-xing. 一类高维向量值双正交小波包 [J]. 河北大学学报(自然科学版) 2006.doi:10.3969/j.issn.1000-1565.2006.06.002
[3] Sam Efromovich, Joe Lakey, Maria Cristina Pereyra, Nathaniel Tymes. Data-Driven and Optimal Denoising of a Signal and Recovery of Its Derivative Using Multiwavelets [J]. IEEE Transactions on Signal Processing: A publication of the IEEE Signal Processing Society 2004, 3(3).
[4] BACCHELLI S, COTRONEI M, SAUER T. Wavelets for multichannel signals [J]. Advances in Applied Mathematics 2002, 29.
[5] MICCHELLI C A, SAUER T. Regularity of multiwavelets [J]. Advances in Computational Mathematics 1997, 7.