Recently, weighted nuclear norm minimization (WNNM), which regularizes singular values of an input matrix with different strengths according to given weights, has demonstrated impressive results in low-level vision tasks such as additive Gaussian noise removal, deblurring and image inpainting [14, 15, 33]. In this study, we apply WNNM to remove additive Cauchy noise in images. A variational model is adopted based on maximum a posteriori estimate, which contains a data fidelity term that is appropriate for noise following the Cauchy distribution. Weighted nuclear norm is used as a regularizer in the proposed algorithm, and we utilized similar patches in the image by nonlocal similarity. We adopted the nonconvex alternating direction method of multiplier to solve the problem iteratively. Numerical experiments are presented to demonstrate the superior denoising performance of our algorithm compared with other existing methods in terms of quantitative measure and visual quality.

最近，加权核规范最小化（WNNM）根据给定的权重将具有不同强度的输入矩阵的奇异值进行正则化，已在低级视觉任务（例如加性高斯噪声去除，去模糊和图像修补）中显示出令人印象深刻的结果[14， 15、33]。在这项研究中，我们应用WNNM去除图像中的附加柯西噪声。采用基于最大后验估计的变分模型，该模型包含适合于遵循柯西分布的噪声的数据保真度项。加权核范数在该算法中被用作正则化器，并且我们通过非局部相似性在图像中使用了相似的补丁。我们采用乘法器的非凸交变方向方法来迭代解决该问题。