Low-rank tensor completion (LRTC) aims to impute the missing entries from partially observed tensor data, among which low-rankness is of vital importance to get satisfactory results. In this letter, we propose a hierarchical low-rank factorization framework for high-order tensors. For the first layer, the low TR rank is exploited, and for the second layer the low-rankness of each TR core is further considered. With the hierarchical model, the low-rankness of the original tensor can be fully utilized and thus achieving better completion performance. Experimental results on synthetic data and on inpainting tasks using various datasets demonstrate the superior performance and efficiency of our proposed method as compared to the state-of-the-art algorithms.

中文翻译：

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高阶张量的分层分解策略及其在数据补全中的应用

低秩张量完成（LRTC）旨在从部分观察到的张量数据中估算缺失的条目，其中低秩对于获得满意的结果至关重要。在这封信中，我们为高阶张量提出了一个分层的低秩分解框架。对于第一层，利用了低 TR 秩，对于第二层，进一步考虑了每个 TR 核的低秩。通过分层模型，可以充分利用原始张量的低秩，从而获得更好的补全性能。与最先进的算法相比，合成数据和使用各种数据集的修复任务的实验结果证明了我们提出的方法的优越性能和效率。