论文标题
颜色图像通过可靠的纯四元素矩阵完成插图：错误绑定和加权损失
Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss
论文作者
论文摘要
在本文中，我们将颜色图像插入式彩色图像作为纯季基矩阵完成问题。在文献中，季节矩阵完成的理论保证并不确定。我们的主要目的是提出一个新的最小化问题，将核定常和二次损失在三个渠道之间加权。为了填补理论空缺，我们获得了在干净和损坏的政权中绑定的错误，这依赖于四粒矩阵的一些新结果。在强大的完成中考虑了一般的高斯噪音，在所有观察结果都被损坏。由于界限的动机，我们建议通过二次损失的跨渠道重量来处理不平衡或相关的噪声，这是重新平衡噪声水平或消除噪声相关性的主要目的。提供了有关合成和颜色图像数据的广泛实验结果，以确认和证明我们的理论发现。
In this paper, we study color image inpainting as a pure quaternion matrix completion problem. In the literature, the theoretical guarantee for quaternion matrix completion is not well-established. Our main aim is to propose a new minimization problem with an objective combining nuclear norm and a quadratic loss weighted among three channels. To fill the theoretical vacancy, we obtain the error bound in both clean and corrupted regimes, which relies on some new results of quaternion matrices. A general Gaussian noise is considered in robust completion where all observations are corrupted. Motivated by the error bound, we propose to handle unbalanced or correlated noise via a cross-channel weight in the quadratic loss, with the main purpose of rebalancing noise level, or removing noise correlation. Extensive experimental results on synthetic and color image data are presented to confirm and demonstrate our theoretical findings.
