基于截断平衡展开核范数的鲁棒张量环填充

低秩张量填充旨在基于不同张量分解模型恢复缺失数据,由于在挖掘一些高阶数据结构的具有明显的优势,低秩张量环模型已经被广泛应用于张量填充问题。先前的研究已经提出很多关于张量核范数的定义。然而,它们不能很好地近似张量真实的秩,也不能在优化环节利用低秩特性。因此,基于很好近似张量秩的截断平衡展开核范数,提出一种基于截断平衡展开核范数的鲁棒张量环填充模型。在算法优化部分,利用以前提出的矩阵奇异值分解和交替方向乘子法。实验证明,在图像恢复和视频的背景建模问题上,效果比其他算法好。

Low-rank tensor Completion aims to recover missing data.Due to its obvious advantages in exploiting some higher-order data structures,low-rank tensor ring has been widely used in tensor completion problems.Previous studies have proposed several definitions of tensor nuclear norm.However,they do not properly approximate the true rank of tensors very well.In addition,and take advantage of low-rank properties in optimization.Therefore,this paper proposes a robust tensor ring completion model based on the truncated cyclic unfolding nuclear norm regularization,which ap-proximates the tensor rank well.In the optimization part of the algorithm,this paper exploits the previously proposed matrix singular value decomposition and the alternating direction method of multipliers in optimization.Experiments on image restoration and video background modeling show that our algorithm is better than other algorithms.