IEEE Trans Image Process. 2017 Jul;26(7):3098-3112. doi: 10.1109/TIP.2016.2639781. Epub 2016 Dec 15.
Nonlocal image representation methods, including group-based sparse coding and block-matching 3-D filtering, have shown their great performance in application to low-level tasks. The nonlocal prior is extracted from each group consisting of patches with similar intensities. Grouping patches based on intensity similarity, however, gives rise to disturbance and inaccuracy in estimation of the true images. To address this problem, we propose a structure-based low-rank model with graph nuclear norm regularization. We exploit the local manifold structure inside a patch and group the patches by the distance metric of manifold structure. With the manifold structure information, a graph nuclear norm regularization is established and incorporated into a low-rank approximation model. We then prove that the graph-based regularization is equivalent to a weighted nuclear norm and the proposed model can be solved by a weighted singular-value thresholding algorithm. Extensive experiments on additive white Gaussian noise removal and mixed noise removal demonstrate that the proposed method achieves a better performance than several state-of-the-art algorithms.
非局部图像表示方法，包括基于分组的稀疏编码和块匹配三维滤波，在应用于低级任务时表现出了出色的性能。非局部先验从具有相似强度的补丁组成的每个组中提取。然而，基于强度相似性对补丁进行分组会导致对真实图像的估计产生干扰和不准确性。为了解决这个问题，我们提出了一种基于结构的低秩模型，并使用图核范数正则化。我们利用补丁内部的局部流形结构，并根据流形结构的距离度量对补丁进行分组。利用流形结构信息，建立了图核范数正则化，并将其纳入低秩逼近模型。然后我们证明了基于图的正则化与加权核范数是等价的，并且所提出的模型可以通过加权奇异值阈值算法来求解。在去除加性高斯噪声和混合噪声的实验中，我们验证了所提出的方法优于几种最先进的算法。
