Iterative total variation regularization for image restoration in Besov spaces

Computer Engineering and Applications ›› 2011, Vol. 47 ›› Issue (17): 181-184.

• 图形、图像、模式识别 • Previous Articles Next Articles

Iterative total variation regularization for image restoration in Besov spaces

JIANG Lingling1，YIN Haiqing2

1.College of Mathematics and Computational Science，China University of Petroleum，Dongying，Shandong 257061，China
2.School of Science，Xidian University，Xi’an 710071，China

Received:1900-01-01 Revised:1900-01-01 Online:2011-06-11 Published:2011-06-11

Besov空间下迭代全变差正则化的图像恢复模型

江玲玲1，殷海青2

1.中国石油大学数学与计算科学学院，山东东营 257061
2.西安电子科技大学理学院，西安 710071

Abstract

Abstract: An iterative regularization procedure in Besov spaces for image restoration is generalized.By using a suitable sequence of penalty parameters，the issue of solvability of minimization problems arising in each step of the iterative procedure is solved.The generalized iterative regularization procedure can be considered as a combination of soft-thresholding and hard-thresholding.Moreover，an effective stopping criteria and convergence result for the procedure are obtained.The numerical results indicate that the iteration procedure yields high-quality reconstructions and converges faster than the Xu-Osher method.

Key words: iterative regularization, total variation, Bregman distance, Besov spaces

摘要： 在Besov空间下，提出了一种用于图像恢复领域的迭代全变差正则化模型。通过使用一个加权的参数序列，给出了一个迭代正则化的变分问题，这个变分问题实际上是一个小波软硬阈值结合的迭代程序。给出了新模型的停止标准和一些好的性质，如单调性和收敛性等。数值实验表明与传统去噪方法相比，新方法不仅能较好地恢复图像，而且收敛速度较快。

关键词: 迭代正则化, 全变差, Bregman距离, Besov空间

JIANG Lingling1，YIN Haiqing2. Iterative total variation regularization for image restoration in Besov spaces[J]. Computer Engineering and Applications, 2011, 47(17): 181-184.

江玲玲1，殷海青2. Besov空间下迭代全变差正则化的图像恢复模型[J]. 计算机工程与应用, 2011, 47(17): 181-184.

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Iterative total variation regularization for image restoration in Besov spaces

Besov空间下迭代全变差正则化的图像恢复模型

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