基于小波和变分泛函的图像分解  

Image decomposition based on wavelet and variational functional

作　　者：姜东焕[1] 徐光宝[2] 宋国乡[1] 

机构地区：[1]西安电子科技大学理学院数学系,陕西西安710071 [2]山东科技大学信息科学与工程学院,山东青岛266510

出　　处：《系统工程与电子技术》2007年第6期848-851,共4页Systems Engineering and Electronics

基　　金：国家部委预研基金项目资助课题(51487020203DZ0103)

摘　　要：提出了一种小波域图像分解算法,该算法通过在小波域中最小化一个变分泛函把图像分解成u和v两部分,其中u在Besov空间B11(L1)表示图像的几何特征,v在对偶空间B∞-1(L∞)刻画了零均值振荡信号,如纹理和噪声。在求解泛函最小值时,采用一种新的迭代的子空间投影方法,利用该投影方法得到图像在小波域中的分解部分序列,重构该序列的极限即可得到图像的分解部分,同时给出了该迭代方法的收敛性证明。实验结果表明新模型比Daubechies-Teschke模型能更好地分解图像,尤其是低噪声图像。An algorithm to decompose an image into two components u and v is constructed. The first component u belongs to B1^1 （L1） and it contains geometric information while the second part v is in the dual space B∞^-1 （L∞）, which contains signals with oscillatory patterns of zero mean, such as texture and noise. The decomposition by minimizing a variational functional in the wavelet domain which depends on the two variables u and v. To get the minimizer, a new iterative projection algorithm to obtain the sequence of image decomposition components in the wavelet domain and get the final image decomposition components by reconstructing the limit of the sequence. At the same time, the convergence of the algorithm is shown. Numerical results are presented, showing that the new model decomposes better a given image, possible noisy, than the Daubechies-Teschke model.

关 键 词：图像分解 变分泛函 小波 BESOV空间 

分 类 号：TN911[电子电信—通信与信息系统]