张雷,刘丛.基于可分离字典的稀疏和低秩表示图像去噪[J].包装工程,2022,43(21):153-161.
ZHANG Lei,LIU Cong.Sparse and Low-rank Representation with Separable Dictionary for Image Denoising[J].Packaging Engineering,2022,43(21):153-161. |
| 基于可分离字典的稀疏和低秩表示图像去噪 |
| Sparse and Low-rank Representation with Separable Dictionary for Image Denoising |
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| DOI：10.19554/j.cnki.1001-3563.2022.21.020 |
| 中文关键词: 图像去噪 低秩表示 稀疏表示 可分离字典学习 |
| 英文关键词: image denoising low-rank representation sparse representation separable dictionary learning |
| 基金项目:国家自然科学基金资助项目(61703278) |
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| 中文摘要: |
| 目的 为了有效去除图像中的椒盐噪声，提高图像质量。方法 文中将可分离字典和低秩表示结合，提出基于可分离字典的稀疏和低秩表示算法(SLRR–SD)。首先，使用可分离字典代替传统的过完备字典可分离字典可以对二维图像直接表示。其次，使用Frobenius范数对分离字典进行约束以挖掘字典内部的低秩性。此外，为了挖掘图像内部的稀疏结构，对表示系数使用稀疏约束进一步提升表示的有效性。结果 提出的算法在噪声强度为5%、10%、20%和30%下，PSNR/FSIM的平均值分别为32.736/0.975、29.769/0.957、29.295/0.951和26.768/0.921。结论 文中算法保留了相邻列之间的相关性，并且可分离字典优化过程也降低了计算负担。实验结果表明，该算法在保留原图像信息的同时能更好地完成去噪任务。 |
| 英文摘要: |
| The work aims to effectively remove the salt and pepper noise in the image and improve the image quality. Separable dictionary and low-rank representation were combined to propose a sparse and low-rank representation with separable dictionary for image denoising (SLRR-SD). Firstly, the traditional overcomplete dictionary was replaced by a separable dictionary, which could directly represent two-dimensional images. Secondly, the Frobenius norm was used to separate dictionary constraints to mine the low-rankness inside the dictionary. In addition, in order to mine the sparse structure inside the image, the effectiveness of the representation was further improved by sparse constraints on the representation coefficients. The mean values of PSNR and FSIM of the proposed algorithm at 5%, 10%, 20% and 30% noise intensity were 32.736/0.975, 29.769/0.957, 29.295/0.951 and 26.768/0.921, respectively. The algorithm proposed preserves the correlation between adjacent columns. The optimization process of separable dictionary also reduces the computational burden. The experimental results show that the algorithm can better complete the denoising task while retaining the original image information. |
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