数学物理学报 ›› 2009, Vol. 29 ›› Issue (4): 882-890.

• 论文 • 上一篇    下一篇

图像恢复问题中减少梯子现象的一种新模型

  

  1. (1. 中国科学院 数学与系统科学研究院应用数学所, 北京 100190, 2. 中国石油大学(华东) 数学院, 山东 东营 257061)
  • 收稿日期:2007-01-22 修回日期:2008-09-25 出版日期:2009-08-25 发布日期:2009-08-25

A New Model for Staircase Reduction in Image Restoration Problems

  1. (1. Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, 2. Department of Mathematics, China University of Petroleum, Shandong, Dongying 257061)
  • Received:2007-01-22 Revised:2008-09-25 Online:2009-08-25 Published:2009-08-25

摘要:

自从Rudin,Osher和Fatemi提出图像处理的经典模型--- ROF模型, 总变差模型成为图像处理中一个普遍有效的工具. 总变差模型具有保留边界轮廓的优点, 但同时也导致了光滑边界的不连续性, 即梯子现象. 该文在ROF模型的基础上, 针对梯子现象, 提出一种新的图像去噪模型, 并且利用一种新的对偶方法对问题进行求解. 数值实验证明, 新的模型保留了ROF模型的优点, 同时明显地减少了梯子现象.

关键词: 图像恢复, 总变差, 对偶方法,  欧拉方程

Abstract:

In this paper, the authors propose a new model for image restoration problems, based on the total variation minimizing models proposed by Rudin, Osher, and Fatemi(ROF). Since the functional is nonquadratic, the dual method and Newton's method are used to compute the regularized solutions.The numerical experiments show the improvement is fairly valid.

Key words: Image restoration, Total variation, Dual method, Euler equation

中图分类号: 

  • 68U10