| 基于交叠组合稀疏双正则项的全变分图像复原 |
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| 引用本文： | 蔡江乾,蔡光程.基于交叠组合稀疏双正则项的全变分图像复原[J].教育技术导刊,2020,19(7):204-209. |
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| 作者姓名： | 蔡江乾 蔡光程 |
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| 作者单位： | 昆明理工大学 理学院，云南 昆明 650500 |
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| 基金项目： | 国家自然科学基金项目（11461037） |
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| 摘 要： | 为减少图像复原中产生的阶梯效应和边缘模糊现象，引入 Hessian 矩阵，设计带有交叠组合稀疏化的双正则项。采用一阶交叠组合稀疏的正则项保留边缘，同时采用二阶交叠组合稀疏的正则项缓解一阶正则项产生的阶梯效应；通过构造两个可分离算子最小化问题求解图像复原问题，在乘子交替方向法（ADMM）的框架下，得出求解各子问题的迭代形式，并提出新的复原算法。实验结果表明，峰值信噪比比传统方法至少提高了0.8dB，结构相似度指数最高达 0.9，最低为 0.72。新算法在去除噪声的同时，有效保留了图像纹理信息。
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| 关 键 词： | 图像复原 交叠组合稀疏 全变分 二阶正则项 乘子交替方向法 |
| 收稿时间： | 2020-05-22 |
Image Restoration Using Total Variation with Two Overlapping Group Sparsity Regularizers |
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| CAI Jiang-qian,CAI Guang-cheng.Image Restoration Using Total Variation with Two Overlapping Group Sparsity Regularizers[J].Introduction of Educational Technology,2020,19(7):204-209. |
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| Authors: | CAI Jiang-qian CAI Guang-cheng |
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| Institution: | Faculty of Science，Kunming University of Science and Technology，Kunming 650500，China |
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| Abstract: | To reduce the staircase effect and the edge blur in the image restoration，the Hessian matrix is introduced to design two over?lapping group sparsity regularizers. The idea is to preserve edges by using the first order term，and remove the staircase effect by using the second order term. Then the image restoration is achieved by constructing the minimization problem of two separable operators. In the framework of the alternating directions method of multipliers（ADMM），the iterative form of the solution of each subproblem is ob? tained by deducing the optimization condition，and a new restoration algorithm is proposed. The experimental result demonstrates that the peak signal-to-noise ratio is improved by at least 0.8dB by comparing the traditional method，and the structure similarity index is as high as 0.9 and as low as 0.72. The new algorithm effectively retains the texture information of the image while removing the noise. |
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| Keywords: | image restoration overlapping group sparsity total variation second order regularizer ADMM |
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