基于变分的图像恢复算法及收敛性  

ALGORITHM FOR IMAGE RESTORATION BASED ON VARIATION AND ITS CONVERGENCE

作　　者：张永平[1] 郑南宁[2] 赵荣椿[3] 

机构地区：[1]陕西师范大学数学系,西安710062 [2]西安交通大学人工智能与机器人研究所,西安710049 [3]西北工业大学计算机系,西安710072

出　　处：《自动化学报》2002年第5期673-680,共8页Acta Automatica Sinica

基　　金：国家创新研究群体科学基金 (60 0 2 43 0 1 );国家自然科学基金 (60 1 75 0 0 6)资助

摘　　要：提出了一种保持边缘的正则化图像恢复算法 ,该方法可有效地用于求解线性逆问题的非凸优化过程 .通过对正则化函数及相应泛函性质的理论分析 ,得出了使泛函达到最小的正则化函数表达式 ;引入一个与原非凸泛函相应的二元泛函 ,将非凸优化问题转化为本质上的凸优化问题 ,采用松弛迭代算法获得非凸优化问题的局部极小解 ;证明了所提出的算法是全局收敛的 .A new algorithm for edge-preserving image restoration is presented in this paper. The variation based method can be effectively used in the process of non-convex optimization for solving the linear inverse problem. By analyzing the properties of regularization functions and the corresponding energy functional, an optimal expression of regularization function and a new energy functional with binary variables are introduced. Thus the non-convex optimization problem is transformed into a sequence of essentially convex one. The local optimal solution of no-convex optimization problem is then obtained by using a relaxation iterative algorithm. Such algorithm is shown to be globally convergent. Finally, the proposed method is tested on real and synthetic images.

关 键 词：变分 图像恢复算法 收敛性 正则化 变分 全局收敛 图像信息处理 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]