MATLAB中5/3小波计算模型所得系数冗余问题分析  

ANALYSING COEFFICIENTS REDUNDANCY DERIVED FROM 5/3 WAVELET TRANSFORM MODEL IN MATLAB

作　　者：李飞[1] 薛健[1] 

机构地区：[1]北京交通大学电子信息工程学院,北京100044

出　　处：《计算机应用与软件》2013年第4期267-270,286,共5页Computer Applications and Software

摘　　要：MATLAB小波工具箱中,并未给出双正交小波计算模型,而是将滤波器系数补零延拓为相同的偶数长度后,直接采用正交小波的模型进行计算。针对5/3小波采用该类模型处理非周期信号,对于奇起点的偶数长信号和偶起点的奇数长信号,分解所得系数中2个近似系数和1个细节系数冗余;对于奇起点的奇数长信号和偶起点的偶数长信号,所得系数中有1个近似系数冗余,从而增大数据存储量和计算量,降低重构精度的问题。在分析MATLAB所给算法基础上,提出改进算法,当该算法分解尺寸为1024×1024(像素×像素)的图像至第6级时,较MATLAB所给算法便可少计算10174个系数,且重构图像的精度也更高。In MATLAB wavelet toolbox,there is no biorthogonal wavelet algorithm model.Instead,the orthogonal wavelet algorithm model is directly used in calculation after the filter coefficient being zero-padded and extended to same even length.Aiming at 5/3 wavelet,the model of that kind is adopted to process the non-periodic signals,for the signals with length of even but odd starting point and with odd length but starting point of even,there are two approximate coefficients and one detail coefficient redundancy in coefficients derived from the decomposition;for the signals with odd length but odd starting point and with even length but starting point of even,there is one approximate coefficient redundancy in derived coefficients,these lead to the problems of increasing data storage and computation complexity and reducing reconstructing precision.In view of that,based on the analysis of the algorithm given by MATLAB,this paper proposes the improved algorithm.Compared with the algorithm in MATLAB wavelet toolbox,when the algorithm decomposing the image in size of 1024×1024（pixels×pixels） to 6th level,there would be 10174 coefficients less computed,and the precision of the reconstructed image is higher as well.

关 键 词：5 3小波 近似系数 细节系数 MATLAB小波工具箱 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]