J4 ›› 2011, Vol. 38 ›› Issue (3): 155-158+163.doi: 10.3969/j.issn.1001-2400.2011.03.025

• 研究论文 • 上一篇    下一篇

带Besov忠诚项的图像去噪变分模型

张伟斌1,2;冯象初1;王卫卫1
  

  1. (1. 西安电子科技大学 理学院,陕西 西安  710071;
    2. 宁夏大学 数学计算机学院,宁夏 银川  750021)
  • 收稿日期:2010-04-26 出版日期:2011-06-20 发布日期:2011-07-14
  • 通讯作者: 张伟斌
  • 作者简介:张伟斌(1973-),男,副教授,西安电子科技大学博士研究生,E-mail: zhangwb@nxu.edu.cn.
  • 基金资助:

    国家自然科学基金资助项目(NSFC 60872138)

Variational model with the Besov fidelity term  for image denoising

ZHANG Weibin 1,2;FENG Xiangchu1;WANG Weiwei1   

  1. (1. School of Science, Xidian Univ., Xi'an   710071, China|
    2. School of Mathematics and Computer, Ningxia Univ., Yinchuan   750021, China)
  • Received:2010-04-26 Online:2011-06-20 Published:2011-07-14
  • Contact: ZHANG Weibin

摘要:

对基于Besov空间的图像去噪模型,利用Besov空间B12,2与Sobolev空间H1的等价关系,引入用Besov模刻画梯度变化的忠诚项,从而得到一类新的图像去噪变分模型.给出了相应的基于小波的数值算法,不需要处理非线性偏微分方程,是一种高效的快速算法.数值实验表明新模型能够获得很好的去噪效果,同时还能够保持图像的边缘和细节.

关键词: 图像去噪, Besov 空间, 小波, Besov忠诚项, 梯度忠诚项

Abstract:

An improved variational model based on Besov space for image denoising is proposed. The L2 fidelity term in the classical model is generalized to the Besov fidelity term. The new model can be quickly solved by using the wavelet thresholding algorithm. The proposed algorithm does not need to solve the nonlinear partial differential equation, so it is an efficient and fast algorithm. Numerical experiments show that this model can remove noise efficiently while preserving the texture and the details.

Key words: image denoising, Besov space, wavelet, Besov fidelity term, gradient fidelity term