In this study, the authors study the problem of tensor completion, in particular for three-dimensional arrays such as visualdata. Previous works have shown that the low-rank constraint can produce impressive performa...
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In this study, the authors study the problem of tensor completion, in particular for three-dimensional arrays such as visualdata. Previous works have shown that the low-rank constraint can produce impressive performances for tensor completion. These works are often solved by means of Tucker rank. However, Tucker rank does not capture the intrinsic correlation of the tensor entries. Therefore, the authors propose a new proximal operator for the approximation of tensor nuclear norms based on tensor-train rank-1 decomposition via the singular value decomposition. The proximal operator will perform a soft-thresholding operation on tensor singular values. In addition, the low-rank constraint can capture the global structure of data well, but it does not exploit local smooth of visualdata. Therefore, they integrate total variation as a regularisation term into low-rank tensor completion. Finally, they use a primal-dual splitting to achieve optimisation. Experimental results have shown that the proposed method, can preserve the multi-dimensional nature inherent in the data, and thus provide superior results over many state-of-the-art tensor completion techniques.
Tensor completion aims at filling in the missing elements of an incomplete tensor based on its partial observations, which is a popular approach for image inpainting. Most existing methods for visual data recovery can...
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Tensor completion aims at filling in the missing elements of an incomplete tensor based on its partial observations, which is a popular approach for image inpainting. Most existing methods for visual data recovery can be categorized into traditional optimization-based and neural network-based methods. The former usually adopt a low-rank assumption to handle this ill-posed problem, enjoying good interpretability and generalization. However, as visualdata are only approximately low rank, handcrafted low-rank priors may not capture the complex details properly, limiting the recovery performance. For neural network-based methods, despite their impressive performance in image inpainting, sufficient training data are required for parameter learning, and their generalization ability on the unseen data is a concern. In this paper, combining the advantages of these two distinct approaches, we propose a tensor Completion neural Network (CNet) for visualdata completion. The CNet is comprised of two parts, namely, the encoder and decoder. The encoder is designed by exploiting the CANDECOMP/PARAFAC decomposition to produce a low-rank embedding of the target tensor, whose mechanism is interpretable. To compensate the drawback of the low-rank constraint, a decoder consisting of several convolutional layers is introduced to refine the low-rank embedding. The CNet only uses the observations of the incomplete tensor to recover its missing entries and thus is free from large training datasets. Extensive experiments in inpainting color images, grayscale video sequences, hyperspectral images, color video sequences, and light field images are conducted to showcase the superiority of CNet over state-of-the-art methods in terms of restoration performance.
Tensor train (TT) decomposition has drawn people's attention due to its powerful representation ability and performance stability in high-order tensors. In this paper, we propose a novel approach to recover the mi...
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Tensor train (TT) decomposition has drawn people's attention due to its powerful representation ability and performance stability in high-order tensors. In this paper, we propose a novel approach to recover the missing entries of incomplete data represented by higher-order tensors. We attempt to find the low-rank TT decomposition of the incomplete data which captures the latent features of the whole data and then reconstruct the missing entries. By applying gradient descent algorithms, tensor completion problem is efficiently solved by optimization models. We propose two TT-based algorithms: Tensor Train Weighted Optimization (TT-WOPT) and Tensor Train Stochastic Gradient Descent (IT-SGD) to optimize TT decomposition factors. In addition, a method named visualdata Tensorization (VDT) is proposed to transform visualdata into higher-order tensors, resulting in the performance improvement of our algorithms. The experiments in synthetic data and visualdata show high efficiency and performance of our algorithms compared to the state-of-the-art completion algorithms, especially in high-order, high missing rate, and large-scale tensor completion situations.
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