区间约束的全变差图像复原和自动参数估计

何川; 胡昌华; 张伟; 师彪

doi:10.3724/SP.J.1004.2014.01804

区间约束的全变差图像复原和自动参数估计

doi: 10.3724/SP.J.1004.2014.01804

1.
西安高新技术研究所西安 710025

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出版历程
- 收稿日期: 2013-08-29
- 修回日期: 2014-03-24
- 刊出日期: 2014-08-20

Box-constrained Total-variation Image Restoration with Automatic Parameter Estimation

1.
Hi-Tech Institute of Xi'an, Xi'an 710025, China

Funds:

Supported by National Natural Science Foundation of China (61174030, 61104223, 61203189, 61374120, 61203007), the Postdoc-toral Science Foundation of China (2012M512147), and National Sci-ence Fund for Distinguished Young Scholars of China (61025014)

摘要

摘要: 因为数字图像的像素仅能取得给定动态范围内的有限值，像素值的区间约束在图像复原中引起广泛关注. 该文研究了带有正则化参数自动估计的区间约束全变差图像复原问题. 通过变量分裂并引入多组辅助变量，区间约束的全变差最小化问题被分解为一系列更易求解的子问题. 随后，交替方向法被用以求解相关的子问题. 根据Morozov偏差准则，在每步迭代中，正则化参数以闭合形式实现自适应更新. 图像复原实验表明，当较高比例的图像像素值位于给定动态范围的边界时，所提方法可以获得更为精确的复原结果.
- 全变差 /
- 区间约束 /
- 变量分裂 /
- 交替方向法
Abstract: The box constraints in image restoration have been arousing great attention, since the pixels of a digital image can attain only a finite number of values in a given dynamic range. This paper studies the box-constrained total-variation (TV) image restoration problem with automatic regularization parameter estimation. By adopting the variable splitting technique and introducing some auxiliary variables, the box-constrained TV minimization problem is decomposed into a sequence of subproblems which are easier to solve. Then the alternating direction method (ADM) is adopted to solve the related subproblems. By means of Morozov0s discrepancy principle, the regularization parameter can be updated adaptively in a closed form in each iteration. Image restoration experiments indicate that with our strategies, more accurate solutions are achieved, especially for image with high percentage of pixel values lying on the boundary of the given dynamic range.
- Total variation (TV) /
- box constraints /
- variable splitting /
- alternating direction method (ADM)

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参考文献(29)

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