具有特殊伸缩矩阵的三元不可分小波的构造  

The Construction of Trivaraiate Nonseparable Wavelets with Special Dilation Matrix

作　　者：黄永东[1] 杨淼[1] 

机构地区：[1]北方民族大学信息与系统科学研究所,银川750021

出　　处：《应用数学学报》2010年第2期247-261,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10961001);教育部科学技术研究重点(209152);宁夏自然科学基金(NZ0846)资助项目

摘　　要：多元小波分析是分析和处理高维数字信号的有力工具.不可分多元小波被广泛地应用在模式识别、纹理分析和边缘检测等领域.本文给出了构造一类特殊伸缩矩阵的紧支撑三元不可分小波的算法,利用该算法得到的小波函数继承了来源于尺度函数和符号函数的对称性和消失矩性质,由于符号函数中的参数选取具有很大的自由度,因此可以根据不同的实际情况来动态地确定符号函数,从而为这类小波在信号处理方面的应用提供了便利.最后给出了相应的数值算例.Multi-dimensional wavelet analysis is powerful instrument to analysis and due to multidimensional digital signal.Nonseparable Multi-dimensional wavelet is widely used in modulation recognition,texture analysis,and boundary check and so on.In this paper, we provides an algorithm of construction of compactly supported trivariate nonseparable wavelet with a class of special dilation matrix,wavelets inherit the symmetry of the corresponding scaling function and satisfy the vanishing moment condition originating in the symbols of the scaling function,As the great degree of freedom in choosing the parameter to the symbol function,we could adaptively determine the symbol function in terms of different situations.Therefore,it is convenient to use this kind of wavelets in signal processing. Finally,an example is also give to demonstrate the general theory.

关 键 词：紧支撑 不可分小波 对称性 消失矩 

分 类 号：O174.2[理学—数学]