优化-最小求解的广义总变分图像复原

徐梦溪; 徐枫; 黄陈蓉; 李铭

doi:10.11834/jig.20110723

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专辑

优化-最小求解的广义总变分图像复原
Image restoration using majorization-minimizaiton algorithm based on generalized total variation
2011年16卷第7期页码：1317-1325
网络首发：2011-07-18，

纸质出版：2011
DOI： 10.11834/jig.20110723
稿件说明：

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徐梦溪, 徐枫, 黄陈蓉, 李铭. 优化-最小求解的广义总变分图像复原[J]. 中国图象图形学报, 2011,16(7):1317-1325. DOI： 10.11834/jig.20110723.

Xu Mengxi, Xu feng, Huang Chenrong, Li Ming. Image restoration using majorization-minimizaiton algorithm based on generalized total variation[J]. Journal of Image and Graphics, 2011, 16(7): 1317-1325. DOI： 10.11834/jig.20110723.

摘要

在代价函数中嵌入总变分正则项是解决图像复原中不适定问题的一种有效方法。但是，总变分正则化考虑的仅是一阶而不是高阶邻域像素变分关系；另外，总变分的开方形式还给基于总变分代价函数的优化带来了困难。为此，提出一种基于优化-最小算法的广义总变分正则化图像复原新方法

以克服目前存在的问题。该方法保留了总变分正则化方法能够除噪声保边缘的重尾特征，同时借鉴了双边总变分双重加权机制，从而推导出总变分正则项在邻域范围上的推广形式。该方法还针对广义总变分正则项优化过程中存在的求解瓶颈，提出采用优化-最小算法求得上界函数以逐次逼近最优解。实验结果表明，该方法取得了较好的复原效果，使改善信噪比指标达到2dB左右。

Abstract

Total variation (TV) regularization is an effective tool to resolve ill-posed problem in image restoration. But the TV only considers the first order variation with the higher order variations ignored. Furthermore

the form of TV induces a difficulty in optimization. Accordingly

a method of image restoration based on generalized TV (GTV) using MM algorithm is proposed to overcome the problems of TV. The GTV has not only the heavy tail property of TV

but also bilateral weights of bilateral TV (BTV). In fact

it is an extended form of the TV. For the optimization problem of GTV

we adopt the majorization-minimization (MM) algorithm to overcome its difficulty. Experimental results show that the proposed method achieves effective performance with about 2dB ISNR (improvement of SNR).