一种新的多小波构造方法
首发时间:2015-12-14
摘要:在小波的理论分析中,由一个函数的伸缩平移生成的基函数而建立起来的多分辨率分析是最基本的内容。标准的多分辨率分析(也称为标量MRA)通常只考虑基函数为标量函数的情况.然而,对应的标量小波无法同时满足紧支撑性、对称性、正交性等性质。多小波是克服这个问题的一个重要途径。另外,由于传统的一维小波在处理二维图像数据过程中,无法实现方向选择。本文我们基于分块对称正交矩阵,提出了一维、二维的二重正交多小波,同时具有紧支撑性、对称性、正交性等性质。
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A New Method for Constructing Multiwavelets
Abstract:In the theory of wavelet analysis, the multiresolution analyss based on scaling and shifting one basic function is a key issue. The traditional multiresolution analysis (also named scalar MRA) usually only considering the basic function is a scalar function. However, the corresponding scalar wavelet can't simultaneously meets the properties of finite support, symmetry, orthogonality and so on. Multiwavelets is an alternative to overcoming this problem. In addition, The traditional one dimensional wavelet can't performing direction selection when processing two dimenional image data. In this paer, based on block symmetric orthogonal matrix, we constructed one dimensional, two dimensional two multiplicity wavelets which have the properties of finite support, symmetric and orthogonality.
Keywords: Wavelet Analysis Multiwavelets Two Dimensional Wavelet
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