论文标题
通过统一转换通过多级完成张量完成
Tensor Completion by Multi-Rank via Unitary Transformation
论文作者
论文摘要
张量完成的关键问题之一是恢复保证所需的统一随机样品条目数量。本文的主要目的是研究$ n_1 \ times n_2 \ times n_3 $基于转换的张量奇异值分解的三阶张量完成，并提供所需的样品条目的数量。我们的方法是利用基础张量的多级量，而不是其在界限中的输出等级。在合成和成像数据集的数值实验中，我们证明了我们提出的对样品条目数量的有效性。此外，我们的理论结果对于在转换的张量奇异值分解下应用于$ n_3 $ dimension的任何统一转换都是有效的。
One of the key problems in tensor completion is the number of uniformly random sample entries required for recovery guarantee. The main aim of this paper is to study $n_1 \times n_2 \times n_3$ third-order tensor completion based on transformed tensor singular value decomposition, and provide a bound on the number of required sample entries. Our approach is to make use of the multi-rank of the underlying tensor instead of its tubal rank in the bound. In numerical experiments on synthetic and imaging data sets, we demonstrate the effectiveness of our proposed bound for the number of sample entries. Moreover, our theoretical results are valid to any unitary transformation applied to $n_3$-dimension under transformed tensor singular value decomposition.
