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.
翻译:单项完成的关键问题之一是回收担保所需的统一随机抽样条目数量。本文的主要目的是根据变色单值分解法,研究美元_1\timen_2\timen_2\timen_3x三阶分解法,并对所需样本条目的数量进行约束。我们的方法是利用下方蒸汽的多级,而不是在捆绑中的管状。在合成和成像数据集的数值实验中,我们展示了我们提议的对样本条目数量约束的有效性。此外,我们的理论结果对在变色单价单值分解法下应用的任何单项转换都是有效的。