由2N点m-ary插值细分法构造m带正交小波-计算机辅助设计与图形.PDF

第29 卷 第2 期 计算机辅助设计与图形学学报 Vol. 29 No.2 2017 年2 月 Journal of Computer-Aided Design Computer Graphics Feb. 2017 由2N 点m-ary 插值细分法构造m 带正交小波 耿 晶, 郑红婵, 宋伟杰 (西北工业大学应用数学系 西安 710129) (gengjing55@163.com) : 为了能够构造具有良好性质的 m 带正交小波, 本文提出一种利用插值细分法构造紧支正交小波的方法. 首 先基于2N 点m-ary 插值细分法构造m 带紧支正交的可细化函数, 该可细化函数的自相关函数是插值细分法的基极限 函数; 然后根据可细化函数构造正交小波, 并研究了正交小波的消失矩性质. 构造算例结果表明, 利用文中方法可 以构造出新的具有更大自由度的含参m 带正交小波, 并证明了该方法的实用性. : 细分法; 小波; 正交小波 : TP391.41 Construction of m-band Orthonormal Wavelets by 2N-point m-ary Interpolatory Subdivision Schemes Geng Jing, Zheng Hongchan, and Song Weijie (Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710129) Abstract: The aim of the paper is to construct an m-band orthonormal wavelet with some good properties. A new method to construct m-band orthonormal wavelets based on m-ary subdivision schemes is presented. First, we construct an m-band orthonormal refinable function based on an m-ary 2N -point interpolatory sub- division scheme, whose basic limit function is the autocorrelation function of the refinable function, and then construct orthonormal wavelets using the orthonormal refinable function. Moreover, the property of vanish- ing moments of the orthonormal wavelets is analyzed. The feasibility of the method is exposed in three ex- amples and a new 2-band orthonormal wavelet with a tension parameter is constructed. Key words: subdivision schemes; wavelets; orthonormal wavelets , . , . , Haar (multi- , 2 resolution analysis, MRA), [1], .