Tensor completion aims to recover missing entries from partial observations for multi-dimensional data. Traditional tensor completion algorithms process the dimensional data by unfolding the tensor into matrices, which breaks the inherent correlation and dependencies in multiple channels and lead to critical information loss. In this paper, we propose a novel tensor completion model for visual multi-dimensional data completion under the tensor singular value decomposition (t-SVD) framework. In the proposed method, tensor is treated as a whole and a truncated nuclear norm regularization is employed to exploit the structural properties in a tensor and hidden information existing among the adjacent channels of a tensor. Besides, we introduce a weighted tensor to adjust the residual error of each frontal slices in consideration of their different recovery statistics. It does enhance the sparsity of all unfoldings of the tensor and accelerates the convergence of the proposed method. Experimental results on various visual datasets demonstrate the promising performance of the proposed method in comparison with the state-of-the-art tensor completion methods.

张量完成的目的是从多维数据的部分观测中恢复丢失的条目。传统的张量完成算法通过将张量展开为矩阵来处理维数据，这破坏了多个通道中固有的相关性和依赖性，并导致严重的信息丢失。在本文中，我们提出了一种新的张量完成模型，用于在张量奇异值分解（t-SVD）框架下进行可视多维数据完成。在提出的方法中，将张量作为一个整体进行处理，并采用截断的核范数正则化来利用张量的结构特性和张量的相邻通道之间存在的隐藏信息。除了，考虑到不同的恢复统计量，我们引入加权张量来调整每个额叶切片的残留误差。它确实增强了张量所有展开的稀疏性，并加速了所提出方法的收敛性。在各种视觉数据集上的实验结果证明，与最新的张量完成方法相比，该方法具有令人鼓舞的性能。