电子学报 ›› 2013, Vol. 41 ›› Issue (12): 2353-2360.DOI: 10.3969/j.issn.0372-2112.2013.12.006

• 学术论文 • 上一篇    下一篇

变分框架下的多尺度图像恢复与重建

唐利明1,2, 黄大荣3   

  1. 1. 重庆科技学院数理学院, 重庆 401331;
    2. 重庆大学数学与统计学院, 重庆 401331;
    3. 重庆交通大学山区桥梁与隧道工程国家重点实验室培育基地, 重庆 400074
  • 收稿日期:2012-10-11 修回日期:2013-01-20 出版日期:2013-12-25 发布日期:2013-12-25
  • 作者简介:唐利明 男,1978年出生于湖北恩施,博士研究生,主要从事基于偏微分方程与变分理论的图像处理方面的研究工作. E-mail:tlmcs78@163.com 黄大荣 男,1978年出生于湖北恩施,教授,博士,主要从事优化理论,可靠性分析,智能交通图像处理等方面的研究工作.
  • 基金资助:

    国家自然科学基金(No.61004118)

Multiscale Image Restoration and Reconstruction in the Framework of Variation

TANG Li-ming1,2, HUANG Da-rong3   

  1. 1. College of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing 401331, China;
    2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China;
    3. National Key Laboratory Incubation Base of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University, Chongqing 400074, China
  • Received:2012-10-11 Revised:2013-01-20 Online:2013-12-25 Published:2013-12-25

摘要: 变分图像分解,通过极小化能量泛函将图像分解为不同的特征分量,可以被应用到图像的恢复和重建.提出了变分框架下的多尺度图像恢复和重建的思想.基于这种思想,首先提出了一个单参数的(BV,G,E)三元变分分解模型,并且理论分析了参数与不同特征分量的尺度的关系.然后将此模型的参数选为一个二进制序列,得到多尺度的(BV,G,E)变分分解.该多尺度变分分解可以将图像分解为一序列图像结构、纹理和噪声.证明了此多尺度分解的收敛性并且基于对偶理论和交替迭代算法给出了其数值求解方法.最后将提出的多尺度的(BV,G,E)变分分解应用到图像恢复和重建,实验结果证实了理论分析的正确性,显示了将此模型进行图像多尺度恢复和重建的有效性,和与一些其他分解模型相比较的优越性.

关键词: 变分图像分解, 图像恢复, 图像重建, 对偶, 多尺度

Abstract: By minimizing the energy functional,we can obtain the variational image decomposition which decomposes image into different characteristic components,and can be used for image restoration and reconstruction.An idea of multiscale image restoration and reconstruction in the framework of variation is proposed.Based on this idea,firstly,a single-parameter (BV,G,E) trituple decomposition model is proposed,and the relationship between the parameter and the scale of each component is studied theoretically.And then,by replacing the parameter with a binary sequence,we achieve a multiscale (BV,G,E) decomposition which can decompose an image into a sequence of image structure,texture and noise.The convergence of this multiscale decomposition is proved,and an efficient numerical method based on the duality theory and alternate iteration algorithm is introduced to solve it.At last,the proposed multiscale (BV,G,E) decomposition is applied for image restoration and reconstruction.Numerical results support the theoretical results and show that the proposed model is efficient for multiscale image restoration and reconstruction,and is superior to some other decomposition models.

Key words: variational image decomposition, image restoration, image reconstruction, duality, multiscale

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