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Further results on tensor nuclear norms
Calcolo, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Dynamic MRI Reconstruction Combining Tensor Nuclear Norm and Casorati Matrix Nuclear Norm
ISMRM Annual Meeting, 2023Low-rank tensor models have been applied in accelerating dynamic magnetic resonance imaging (dMRI). Recently, a new tensor nuclear norm based on t-SVD has been proposed and applied to tensor completion. Inspired by the different properties of the tensor nuclear norm (TNN) and the Casorati matrix nuclear norm (MNN), we introduce a novel dMRI ...
Yinghao Zhang, Yue Hu, Xin Lu
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Tensor Nuclear Norm LPV Subspace Identification
IEEE Transactions on Automatic Control, 2018Linear parameter varying (LPV) subspace identification methods suffer from an exponential growth in number of parameters to estimate. This results in problems with ill-conditioning. In literature, attempts have been made to address the ill-conditioning by using regularization. Its effectiveness hinges on suitable a priori knowledge.
Bilal Gunes +2 more
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Weighted tensor nuclear norm minimization for tensor completion using tensor-SVD
Pattern Recognition Letters, 2020Abstract In this paper, we consider the tensor completion problem, which aims to estimate missing values from limited information. Our model is based on the recently proposed tensor-SVD, which uses the relationships among the color channels in an image or video recovery problem. To improve the availability of the model, we propose the weighted tensor
Yang Mu +4 more
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Unifying tensor factorization and tensor nuclear norm approaches for low-rank tensor completion
Neurocomputing, 2021Abstract Low-rank tensor completion (LRTC) has gained significant attention due to its powerful capability of recovering missing entries. However, it has to repeatedly calculate the time-consuming singular value decomposition (SVD). To address this drawback, we, based on the tensor-tensor product (t-product), propose a new LRTC method-the unified ...
Du S. +4 more
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The Twist Tensor Nuclear Norm for Video Completion
IEEE Transactions on Neural Networks and Learning Systems, 2017In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an ...
Wenrui Hu +4 more
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Truncated nuclear norm minimization for tensor completion
2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM), 2014In this paper, a tensor n-mode matrix unfolding truncated nuclear norm is proposed, which is extended from the matrix truncated nuclear norm, to tensor completion problem. The alternating direction method of multipliers is utilized to solve this optimization problem.
Long-Ting Huang +3 more
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Dynamic MRI Reconstruction via Weighted Tensor Nuclear Norm Regularizer
IEEE Journal of Biomedical and Health Informatics, 2021In this paper, we propose a novel multi-dimensional reconstruction method based on the low-rank plus sparse tensor (L+S) decomposition model to reconstruct dynamic magnetic resonance imaging (dMRI). The multi-dimensional reconstruction method is formulated using a non-convex alternating direction method of multipliers (ADMM), where the weighted tensor ...
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Multiple graphs learning with a new weighted tensor nuclear norm
Neural Networks, 2021As an effective convex relaxation of the rank minimization model, the tensor nuclear norm minimization based multi-view clustering methods have been attracting more and more interest in recent years. However, most existing clustering methods regularize each singular value equally, restricting their capability and flexibility in tackling many practical ...
Xie, Deyan +4 more
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Fast Guaranteed Tensor Recovery with Adaptive Tensor Nuclear Norm
Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial IntelligenceReal-world datasets like multi-spectral images and videos are naturally represented as tensors. However, limitations in data acquisition often lead to corrupted or incomplete tensor data, making tensor recovery a critical challenge. Solving this problem requires exploiting inherent structural patterns, with the low-rank property being particularly ...
Jiangjun Peng +3 more
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