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摘要:
针对基于低秩先验的图像矩阵补全算法无法有效处理结构性缺失图像修复的问题，建立了在观测矩阵上使用双重先验的矩阵补全模型，在低秩先验的基础上引入稀疏先验，以便更好地利用观测矩阵的先验特征。该模型根据行列间的相关性，使用低秩先验对矩阵正则化；根据行列内的相关性，使用稀疏先验对矩阵正则化；为了更加精确地逼近秩函数，使用截断Schatten-p范数替代核范数作为低秩先验，从而提出了融合低秩和稀疏先验的矩阵补全模型，并使用交替方向乘子法有效处理所提模型。实验结果表明：算法修复的图像细节清晰，与截断核范数模型算法相比，峰值信噪比和结构相似度提升范围分别为2%~44%和0.7%~8%。
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关键词:
- 稀疏先验 /
- 矩阵补全 /
- 截断Schatten-p范数 /
- 图像修复 /
- 交替方向乘子法
Abstract:To handle the problem that the image matrix completion algorithm based on low rank prior cannot effectively deal with the structural missing image inpainting, a matrix completion model using double prior on the observation matrix was established. The sparse prior was integrated with low rank prior, so as to make better use of the prior characteristics of the observation matrix. The model used low rank prior and sparse prior to regularize the matrix by using the correlation between rows and columns and within the row and column, respectively. Furthermore, in order to more accurately approximate the rank function, the truncated Schatten-p norm was used to replace the nuclear norm as the low rank prior. Thus, a matrix completion model integrating low rank and sparse prior was proposed, and the alternating direction method of multiplier was used to solve the proposed completion model effectively. The experimental results show that the details of the inpainting image are clear. Compared with the truncated nuclear norm model algorithm, the corresponding improvement ranges of peak signal-to-noise ratio and structure similarity are 2%-44% and 0.7%-8%, respectively.
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图 2 参数p不同取值的PSNR和SSIM值
Figure 2. Value of PSNR and SSIM for different values of parameter p
图 3 混合缺失情况下实验结果图像对比
Figure 3. Image comparison of experimental results in the case of mixed missing
图 4 字符缺失情况下实验结果图像对比
Figure 4. Image comparison of experimental results in the case of character missing
图 5 块状缺失情况下实验结果图像对比
Figure 5. Image comparison of experimental results in the case of blocky missing
表 1 随机缺失情况下4种算法评价指标结果对比
Table 1. Comparison of evaluation index results of four algorithms in the case of random missing
算法 缺失比例 PSNR/dB SSIM LRMC 0.4 29.38 0.862 9 0.6 25.30 0.727 3 0.8 16.31 0.407 0 TNNR 0.4 34.08 0.963 6 0.6 31.56 0.912 9 0.8 28.47 0.795 0 TSPN 0.4 34.16 0.964 8 0.6 31.67 0.913 6 0.8 28.63 0.796 9 TSPN-SR 0.4 35.27 0.968 1 0.6 33.10 0.925 0 0.8 30.67 0.839 9 
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表 2 混合缺失情况下4种算法评价指标结果对比
Table 2. Comparison of evaluation index results of four algorithms in the case of mixed missing
算法 PSNR/dB SSIM LRMC 16.82 0.775 0 TNNR 17.42 0.851 4 TSPN 17.48 0.852 3 TSPN-SR 30.88 0.929 2
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表 3 字符缺失情况下4种算法评价指标结果对比
Table 3. Comparison of evaluation index results of
算法 PSNR/dB SSIM LRMC 27.75 0.929 0 TNNR 27.81 0.974 5 TSPN 27.89 0.976 2 TSPN-SR 30.60 0.988 2
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表 4 块状缺失下4种算法评价指标结果对比
Table 4. Comparison of evaluation index results of four algorithms in the case of blocky missing
算法 PSNR/dB SSIM LRMC 26.30 0.956 6 TNNR 27.31 0.979 5 TSPN 27.37 0.980 5 TSPN-SR 27.98 0.986 4
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