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.
翻译:在本文中,我们研究彩色图象作为纯四环矩阵完成问题。在文献中,四环矩阵完成的理论保障没有很好确立。我们的主要目的是提出一个新的最小化问题,目标是将核规范与四环损失结合到三个渠道之间。为了填补理论空缺,我们在清洁和腐败的制度中都发现了错误,这些错误依赖于四环矩阵的一些新结果。在对所有观测结果都进行腐蚀的情况下,一般高斯语噪音被认为是稳健的完成过程。受错误驱使,我们提议通过跨通道重量处理四环损失中的不平衡或相关噪音,其主要目的是重新平衡噪音水平,或消除噪音相关性。关于合成和彩色图像数据的广泛实验结果将用来证实和展示我们的理论结论。