CoNoT: Coupled Nonlinear Transform-Based Low-Rank Tensor Representation for Multidimensional Image Completion.

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.

Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery.

Recently, transform-based tensor nuclear norm (TNN) minimization methods have received increasing attention for recovering third-order tensors in multi-dimensional imaging problems. The main idea of these methods is to perform the linear transform along the third mode of third-order tensors and then minimize the nuclear norm of frontal slices of the transformed tensor. The main aim of this paper is to propose a nonlinear multilayer neural network to learn a nonlinear transform by solely using the observed tensor in a self-supervised manner. The proposed network makes use of the low-rank representation of the transformed tensor and data-fitting between the observed tensor and the reconstructed tensor to learn the nonlinear transform. Extensive experimental results on different data and different tasks including tensor completion, background subtraction, robust tensor completion, and snapshot compressive imaging demonstrate the superior performance of the proposed method over state-of-the-art methods.