华东师范大学学报(自然科学版) ›› 2007, Vol. 2007 ›› Issue (5): 62-69.

• 数学 统计学 • 上一篇    下一篇

全变分极小与二阶泛函的组合图像恢复模型(英)

黎芳   

  1. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2006-09-29 修回日期:2006-12-25 出版日期:2007-09-25 发布日期:2007-09-25
  • 通讯作者: 黎芳

Image Restoration Combining the Total Variation Minimization and a SecondOrder Functional(English)

LI Fang   

  1. Department of Mathematics, East China Normal University,Shanghai 200062，China
  • Received:2006-09-29 Revised:2006-12-25 Online:2007-09-25 Published:2007-09-25
  • Contact: LI Fang

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摘要： 通过组合全变分极小泛函与一个二阶泛函得到了新的变分模型，用于图像恢复. 相应的负梯度流是一个四阶偏微分方程.此组合模型兼有TV模型和二阶泛函的长处，能够在保持轮廓的同时避免光滑区域出现“块状“效应.数值实验用的是包含轮廓，平坦区域和光滑区域的图像，实验结果说明了此模型的优越性.

关键词: 图像恢复, 全变分, PDE, BV空间, 负梯度流, 图像恢复, 全变分, PDE, BV空间, 负梯度流

Abstract: A new variational model for noise removal was proposed. It combines the total variational (TV) functional with a second order functional,and the corresponding negative gradient flow is a fourth order PDE.The proposed model combines the benefits of the total variation model and the secondorder model,being able to preserve edges while at the same time avoid the staircase effect in smooth regions. Experimental results illustracted advantages of the proposed model.

Key words: total variation, PDE, BV space, negative gradient flow, image restoration, total variation, PDE, BV space, negative gradient flow

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