Abstract: Since nuclear norm tends to underestimate the nonzero singular values in Low-Rank Representation model（LRR）, a parameterized nonconvex penalty function is employed to estimate nonzero singular values. Meanwhile using the ability of Total Variation（TV） norm to preserve image edge information and enhance the smoothness of image region, a new image denoising algorithm is proposed by applying the TV norm constraint to the coefficient matrix in LRR model, and the corresponding model is solved by an alternating minimization method. Exploiting the non-local self-similarity prior inherent in the image, the proposed algorithm can effectively find and remove noise, while enhancing the structure and area smoothness, which improves the quality of the restored image. Experimental results indicate that the proposed algorithm achieves a competitive denoising performance, especially for high-intensity noise, in comparison with state-of-the-art algorithms in terms of objective evaluation and visual effect.

Key words: image denoising, Low?Rank Representation（LRR）, Total Variation（TV） norm, nonconvex penalty function, non-local self-similarity

摘要： 由于低秩表示（Low-Rank Representation，LRR）模型中核范数对非零奇异值的估计不足，所以利用参数化的非凸惩罚函数来估计非零奇异值，同时结合全变差（Total Variation，TV）范数保持图像边缘信息和加强区域平滑性的能力，通过对LRR模型中的系数矩阵施加TV范数约束，提出了一个新的图像去噪算法，并且采取交替最小化方法求解对应模型。利用图像的内在非局部自相似性先验，所提算法能够在有效发现和移除噪声的同时，增强恢复图像的结构和区域平滑性，提高图像的恢复质量。实验结果表明，与其他去噪算法相比，无论是客观评价还是视觉效果，所提算法都实现了具有竞争力的去噪表现，特别是在噪声强度较大时。

关键词: 图像去噪, 低秩表示（LRR）, TV范数, 非凸惩罚函数, 非局部自相似性