Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To further deal with its sensitivity to sparse component as it does in tensor principle component analysis, we propose robust tensor ring completion (RTRC), which separates latent low-rank tensor component from sparse component with limited number of measurements. The low rank tensor component is constrained by the weighted sum of nuclear norms of its balanced unfoldings, while the sparse component is regularized by its $\ell _1$ norm. We analyze the RTRC model and gives the exact recovery guarantee. The alternating direction method of multipliers is used to divide the problem into several sub-problems with fast solutions. In numerical experiments, we verify the recovery condition of the proposed method on synthetic data, and show the proposed method outperforms the state-of-the-art ones in terms of both accuracy and computational complexity in a number of real-world data based tasks, i.e., light-field image recovery, shadow removal in face images, and background extraction in color video.

中文翻译：

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稳健的低阶张量环完成

低秩张量补全基于不同的张量分解来恢复丢失的条目。由于其在开发一些高阶数据结构方面的突出表现，低秩张量环已被应用于张量补全。为了进一步处理其在张量主分量分析中对稀疏分量的敏感性，我们提出了稳健张量环完成（RTRC），它将潜在的低秩张量分量与测量次数有限的稀疏分量分开。低秩张量分量受其平衡展开的核范数的加权和约束，而稀疏分量受其 $\ell _1$ 范数正则化。我们分析了 RTRC 模型并给出了准确的恢复保证。乘法器的交替方向方法用于将问题划分为具有快速解决方案的几个子问题。在数值实验中，我们验证了所提出方法在合成数据上的恢复条件，并表明所提出的方法在许多基于真实世界数据的任务中在准确性和计算复杂度方面均优于最先进的方法，即光场图像恢复、人脸图像中的阴影去除和彩色视频中的背景提取。