伴随伸缩矩阵的二维周期小波框架的构造

Construction of Bidimensional Periodic Wavelet Frames with Dilation Matrix

为了解决二维信号中存储与传输问题,研究了周期小波框架的构造方法.根据酉扩张方案构造出二维小波紧框架,进而得到短支撑二维周期紧小波框架.根据混合扩张方案,从紧支撑的尺度函数对应的滤波器出发,构造出一双对偶小波框架,对它们进行周期化,得到一双短支撑的对偶周期小波框架.

In order to solve the problem of storage and transmission of bidimensional signals,a constructive method of periodic wavelet frames is studied.Bidimensional tight wavelet frames are constructed by the unitary extension principle.Moreover,the compactly supported periodic tight bidimensional wavelet frames are obtained.Also on the basis of the mixed extension principle,a pair of dual wavelet frames is constructed under the condition of compactly supported scaling function filters.The periodization of the dual wavelet frames is still a pair of dual compactly supported periodic wavelet frames.