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摘要:
针对纹理图像的去噪问题,通过分析全变分(TV)去噪模型与方向全变分(DTV)去噪模型,提出了一种具有鲁棒性的基于
的DTV去噪模型。为了刻画图像中的不同结构特征,该模型中DTV正则项的指数p 由图像的结构来确定在(0,2)中自适应地选取。由于该模型是含有可分性算子的非光滑优化问题,可用交替方向乘子法(ADMM)求解,并能保证算法的收敛性。数值实验结果表明:与其他经典模型相比,提出的模型取得了更高的峰值信噪比和结构相似度,在去除噪声的同时能有效保持图像的细节信息。-
关键词:
- 交替方向乘子法(ADMM) /
- 方向全变分(DTV)模型 /
- 图像去噪 /
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(拟)范数图像去噪 / - ROF模型
Abstract:For the problem of texture image denoising, by analyzing the advantages and disadvantages of the total variation (TV) denoising model and the directional total variation (DTV) denoising model, we propose a robust denoising model based on
directional total variation. In the proposed model, in order to efficiently characterize the different structural features in the image, the exponentialp in the edge adaptive directional total variation regularization term can be availably chosen in (0, 2) based on the structure in the image. Since the proposed model is a non-smooth convex optimization with separable operator, it can be solved by using the alternating direction method of multipliers (ADMM). Then the convergence of the numerical method can be efficiently kept. Compared with other classic models, numerical implementations show that the proposed model can achieve higher peak signal-to-noise ratio and structural similarity, and can effectively retain image details while removing noise. -
表 1 不同去噪模型去噪后所得的SNR和SSIM比较
Table 1. Comparison of SNR and SSIM obtained after denoising by different denoising models
图像 模型 SNR/dB SSIM σ=0.01 σ=0.05 σ=0.1 σ=0.01 σ=0.05 σ=0.1 图 4(a) ROF 18.846 5 14.873 3 13.415 7 0.757 9 0.461 0 0.332 2 DTV 19.823 9 15.971 4 14.301 1 0.792 0 0.554 5 0.428 4 ADMM-DTV 19.896 0 16.060 4 14.381 1 0.796 2 0.560 1 0.438 9 DTVP 19.923 1 16.219 2 14.607 0 0.800 0 0.591 5 0.484 1 图 4(b) ROF 21.350 5 19.210 5 18.414 8 0.652 1 0.511 8 0.462 0 DTV 21.530 8 19.344 0 18.478 3 0.673 2 0.532 0 0.483 0 ADMM-DTV 21.804 4 19.842 5 19.149 4 0.682 2 0.553 5 0.508 3 DTVP 22.024 1 20.224 6 19.509 4 0.701 4 0.578 0 0.534 2 图 4(c) ROF 19.094 0 12.534 0 09.684 7 0.982 6 0.922 5 0.854 2 DTV 19.314 8 12.755 5 9.880 8 0.983 5 0.926 2 0.860 4 ADMM-DTV 19.537 1 12.908 6 10.054 3 0.984 3 0.928 6 0.865 5 DTVP 20.251 9 13.567 8 10.446 6 0.986 6 0.938 3 0.876 1 图 4(d) ROF 19.428 8 14.903 9 13.196 0 0.851 0 0.642 0 0.486 9 DTV 20.483 1 15.805 8 13.887 4 0.884 4 0.703 9 0.573 8 ADMM-DTV 20.699 0 16.016 1 14.011 2 0.889 1 0.712 0 0.586 4 DTVP 20.925 7 16.325 7 14.357 3 0.896 1 0.740 7 0.622 7 -
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