In this work, we consider the tensor completion problem of an incomplete and noisy observation. We introduce a novel completion model using bilevel minimization. Therefore, bilevel model-based denoising for the tensor completion problem is proposed. The denoising and completion tasks are fully separated. The upper-level directly addresses the completion problem with the truncated nuclear norm, while the lower-level uses the sparsity prior which is characterized by the l₁-norm for the denoising task. Furthermore, we propose a simple strategy to solve our bilevel optimization problem. It formulates the lower-level as a fixed-point equation and then applies a simple but efficient iterative algorithm to get the reconstructed tensor. Numerically, the superiority of the proposal is reported via several experiments conducted on real data with an extremely small subset of observed entries.

在这项工作中，我们考虑了一个不完整且嘈杂的观测值的张量完成问题。我们介绍了一种使用双层最小化的新颖完成模型。因此，提出了针对张量完成问题的基于两级模型的去噪方法。去噪和完成任务完全分开。上级直接使用截断的核规范来解决完工问题，而下级使用稀疏优先级，其特征是l ₁-规范去噪任务。此外，我们提出了一种简单的策略来解决我们的双层优化问题。它将下层公式表述为不动点方程，然后应用简单但有效的迭代算法来获取重构的张量。从数字上讲，该提案的优越性是通过对真实数据进行的几次实验报告的，其中观察到的条目非常少。