为解决加权核范数最小化(WNNM)图像去噪无法较好地表达复杂和不规则的图像结构,易产生过平滑现象的问题,将相对全变差(RTV)融入加权核范数最小化,对WNNM低秩表示模型施加RTV范数约束,提出一种RTV-WNNM图像去噪模型,采取交替方向乘子(ADMM)算法迭代求解对应模型,获得清晰图像。将提出的新方法与多种基于低秩矩阵近似的去噪算法进行比较,所提算法在保持图像边缘和加强区域平滑性方面有较好的性能,特别是在高密度图像噪声影响下,算法性能也能得到大幅提升。实验结果表明,加入RTV范数的低秩去噪模型具有良好的恢复图像结构能力,能较好地提高去噪性能。

Image denoising using weighted nuclear norm minimization (WNNM) is prone to over-smoothing and cannot distinguish intricate and irregular image structures effectively. Image denoising model using relative total variation (RTV) WNNM is proposed. The proposed denoising method, which utilizes the alternate direction multiplier (ADMM) algorithm to solve the corresponding model iteratively, can obtain a clear image. The ADMM algorithm integrates RTV into WNNM and applies the RTV norm constraint to the low-rank representation model of WNNM. Compared to several state-of-the-art denoising methods based on low-rank matrix approximation, the proposed method improves image denoising performance, maintains image edges effectively, and enhances smoothness, particularly for images with high-density noise. Experimental results demonstrate that the proposed method with RTV norm restores image structure effectively and improves denoising performance.