Tensor train (TT) representation has achieved tremendous success in visual data completion tasks, especially when it is combined with tensor folding. However, folding an image or video tensor breaks the original data structure, leading to local information loss as nearby pixels may be assigned into different dimensions and become far away from each other. In this paper, to fully preserve the local information of the original visual data, we explore not folding the data tensor, and at the same time adopt graph information to regularize local similarity between nearby entries. To overcome the high computational complexity introduced by the graph-based regularization in the TT completion problem, we propose to break the original problem into multiple sub-problems with respect to each TT core fiber, instead of each TT core as in traditional methods. Furthermore, to avoid heavy parameter tuning, a sparsity promoting probabilistic model is built based on the generalized inverse Gaussian (GIG) prior, and an inference algorithm is derived under the mean-field approximation. Experiments on both synthetic data and real-world visual data show the superiority of the proposed methods.

翻译：张量列（TT）表示在视觉数据补全任务中取得了巨大成功，尤其是当它与张量折叠相结合时。然而，对图像或视频张量进行折叠会破坏原始数据结构，导致局部信息丢失，因为邻近像素可能被分配到不同维度而彼此远离。在本文中，为了充分保留原始视觉数据的局部信息，我们探索不折叠数据张量，同时采用图信息对邻近条目之间的局部相似性进行正则化。为了克服基于图的正则化在TT补全问题中引入的高计算复杂度，我们提出将原始问题分解为多个关于每个TT核心纤维的子问题，而非传统方法中关于每个TT核心的子问题。此外，为避免繁重的参数调整，基于广义逆高斯（GIG）先验构建了促进稀疏性的概率模型，并在平均场近似下推导出推理算法。在合成数据和真实世界视觉数据上的实验均表明了所提出方法的优越性。