分级(BV,W^(-1,∞))分解的多尺度图像表示  

Multiscale Representation of Image Using Hierarchical (BV,W^(-1,∞)) Decomposition

作　　者：卢成武[1,2] 宋国乡[2] 宋宜美[2] 

机构地区：[1]重庆文理学院数学与统计学院,永川402160 [2]西安电子科技大学理学院,西安710071

出　　处：《工程数学学报》2009年第4期601-608,共8页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(60872138);重庆市教委科学技术研究项目(KJ091208);重庆文理学院重点科研项目(Z2008SJ13)

摘　　要：在经典变分图像分解模型中,平衡参数通常依据图像振荡分量的先验信息进行选取。本文针对这一局限性,以更为一般的一类Meyer分解模型为出发点,首先讨论了该模型解的存在性和唯一性,然后给出一种能依据图像自身信息,自适应地确定平衡参数的分级分解框架,进而得到一种分级多尺度图像表示方法,最后,对其收敛性进行了理论分析。并利用Chambolle的投影方法给出具体算法。数值实验结果表明,该方法能较好地弥补单尺度分解模型在图像应用中存在的一些不足。In the image decomposition method based on the variational calculus, the classical selection method for the balance parameter is based on the information of the oscillating component of the image. However, this apriority can＇t be easily obtained in practice. To overcome this defect, we use a more general Meyer＇s decomposition model as start point, the existence and the uniqueness of this model are firstly examined. And then, under a hierarchical multiscale decomposition frame, the selecting for the balance parameter is adapted to the nature of the information of the image. Moreover, a hierarchical multi-scale representation of the image is achieved. Finally, following Chambolle＇s projection algorithm, the convergence of an iterative numerical implementation is proved. The experimental results show that above method can well complement the monoscale decomposition in the application of the image processing.

关 键 词：分级多尺度分解 有界变差 Soblev空间 下半连续 

分 类 号：TN911.73[电子电信—通信与信息系统]