Recently, the transform-based tensor nuclear norm (TNN) methods have shown promising performance and drawn increasing attention in tensor completion (TC) problems. The main idea of these methods is to exploit the low-rank structure of frontal slices of the tensor under the transform. However, the transforms in TNN methods usually treat all modes equally and do not consider the different traits of different modes (i.e., spatial and spectral/temporal modes). To address this problem, we suggest a new low-rank tensor representation based on the coupled nonlinear transform (called CoNoT) for a better low-rank approximation. Concretely, spatial and spectral/temporal transforms in the CoNoT, respectively, exploit the different traits of different modes and are coupled together to boost the implicit low-rank structure. Here, we use the convolutional neural network (CNN) as the CoNoT, which can be learned solely from an observed multidimensional image in an unsupervised manner. Based on this low-rank tensor representation, we build a new multidimensional image completion model. Moreover, we also propose an enhanced version (called Ms-CoNoT) to further exploit the spatial multiscale nature of real-world data. Extensive experiments on real-world data substantiate the superiority of the proposed models against many state-of-the-art methods both qualitatively and quantitatively.

中文翻译：

---

CoNoT：用于多维图像补全的基于耦合非线性变换的低秩张量表示


最近，基于变换的张量核范数（TNN）方法在张量完成（TC）问题中表现出了良好的性能并引起了越来越多的关注。这些方法的主要思想是利用变换下张量的额叶切片的低阶结构。然而，TNN 方法中的变换通常平等地对待所有模式，并且不考虑不同模式（即空间和频谱/时间模式）的不同特征。为了解决这个问题，我们提出了一种基于耦合非线性变换（称为 CoNoT）的新的低秩张量表示，以获得更好的低秩近似。具体来说，CoNoT 中的空间和频谱/时间变换分别利用不同模式的不同特征，并将其耦合在一起以增强隐式低秩结构。在这里，我们使用卷积神经网络（CNN）作为 CoNoT，它可以以无监督的方式仅从观察到的多维图像中学习。基于这种低秩张量表示，我们构建了一个新的多维图像补全模型。此外，我们还提出了一个增强版本（称为 Ms-CoNoT），以进一步利用现实世界数据的空间多尺度性质。对现实世界数据的广泛实验在定性和定量上证实了所提出的模型相对于许多最先进方法的优越性。