基于双核范数最小化的低秩张量填充
Robust Low-Rank Tensor Completion via Double Nuclear Norm Minimization
摘要: 近年来，许多基于张量核范数的方法被提出解决张量填充的问题，并在图像和视频修复任务中受到了极大的关注。但是，核范数优化过程中会存在过度收缩问题。为了解决这个问题，通过可逆线性变换的张量积和张量奇异值分解，提出了基于张量分解的双核范数，证明了张量Schatten-p (p = 1/2)范数与张量双核范数的一致性，构造了双核范数正则化张量填充模型，并且通过交替方向乘子法求解优化模型。在合成数据和真实世界的数据集上的实验结果，可以看出所提出的算法比目前最优的张量填充方法更有效。
Abstract: Recently, methods based on tensor nuclear norm are proposed to address the issue of tensor completion, which have received great attention in the inpainting tasks of image and video. However, excessive shrinkage problem exists in the process of nuclear norm optimization. In order to solve this issue, with tensor-tensor product and tensor singular value decomposition based on inverse linear transforms, tensor double nuclear norm based on tensor factorization is defined. We also prove that it is equivalent to tensor Schatten-p (p = 1/2) norm and propose a double nuclear norm regularized tensor completion (DNTC) model. ADMM is used to solve this optimization model. It’s shown that the proposed method is more accurate and effective than the state-of-the-art methods for tensor completion through the experimental results on synthetic and real data sets.
文章引用：张军, 李峥儿, 姜伟. 基于双核范数最小化的低秩张量填充[J]. 应用数学进展, 2022, 11(1): 442-449. https://doi.org/10.12677/AAM.2022.111052

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