The aim of this paper is to introduce a novel similarity measure using fractional-order derivative for patch comparison in low-rank image denoising approach. Recently, several outstanding low-rank image denoising algorithms have been proposed. However, these methods have limitations in the sense that certain irrelevant patches can be selected during patch comparison. These undesired patches affect singular values shrinkage and aggregation phases of these approaches. Thus, the fine details and edges of denoised image may not be well preserved. To address this issue, a novel method is proposed in which gradient information is injected in patch comparison using discretized fractional-order derivatives. The advantages of proposed approach are twofold: firstly, the patch comparison becomes more reliable by combining intensity and gradient information; secondly, the fractional-order gradient provides an additional degree of freedom to quantify the gradient information for patch comparison in an efficient way. In addition, the proposed algorithm estimates noise level using geometric details encoded in the image patches. The noise estimation strategy may help in terminating the iterative low-rank approximation. Experimental results on test images reveal that the proposed method performs better than several outstanding algorithms, specifically, in the presence of severe noise levels.

本文的目的是在低秩图像去噪方法中引入一种使用分数阶导数进行补丁比较的新相似性度量。最近，已经提出了几种出色的低秩图像去噪算法。然而，这些方法在补丁比较期间可以选择某些不相关的补丁的意义上存在局限性。这些不需要的补丁会影响这些方法的奇异值收缩和聚合阶段。因此，去噪图像的精细细节和边缘可能无法得到很好的保留。为了解决这个问题，提出了一种新方法，其中使用离散分数阶导数在补丁比较中注入梯度信息。所提出方法的优点有两个：首先，通过结合强度和梯度信息，块比较变得更加可靠；其次，分数阶梯度提供了额外的自由度，以有效的方式量化梯度信息以进行补丁比较。此外，所提出的算法使用在图像块中编码的几何细节来估计噪声水平。噪声估计策略可能有助于终止迭代低秩近似。在测试图像上的实验结果表明，所提出的方法比几种优秀的算法性能更好，特别是在存在严重噪声水平的情况下。噪声估计策略可能有助于终止迭代低秩近似。在测试图像上的实验结果表明，所提出的方法比几种优秀的算法性能更好，特别是在存在严重噪声水平的情况下。噪声估计策略可能有助于终止迭代低秩近似。在测试图像上的实验结果表明，所提出的方法比几种优秀的算法性能更好，特别是在存在严重噪声水平的情况下。