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arXiv 2202.02063cs.CVmath.STstat.TH
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彩色图像修补的鲁棒纯四元数矩阵补齐:误差界和加权损失

Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss

The University of Hong Kong(香港大学)

Junren Chen, Michael K. Ng

摘要:

本文将彩色图像修补问题作为一个纯四元数矩阵补齐问题进行研究。在文献中,四元数矩阵完备化的理论保证并不完善。我们的主要目的是提出一个新的最小化问题的目标结合核范数和三个通道之间的二次损失加权。为了填补这一理论空白,我们利用四元数矩阵的一些新结果,得到了在干净和损坏两种情况下的误差界。一般的高斯噪声被认为是在鲁棒完成,其中所有的观察是损坏的。受误差界的启发,我们建议通过二次损失中的跨信道权重来处理不平衡或相关噪声,其主要目的是重新平衡噪声水平或去除噪声相关性。合成和彩色图像数据的广泛的实验结果,以确认和证明我们的理论研究结果。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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