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Tensor p-Shrinkage Nuclear Norm for Low-Rank Tensor Completion [PDF]

Neurocomputing, 2020
In this paper, a new definition of tensor p-shrinkage nuclear norm (p-TNN) is proposed based on tensor singular value decomposition (t-SVD). In particular, it can be proved that p-TNN is a better approximation of the tensor average rank than the tensor nuclear norm when p < 1.
Chunsheng Liu, Hong Shan, Chunlei Chen
exaly   +4 more sources

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Truncated nuclear norm minimization for tensor completion

2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM), 2014
In 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.
Longting Huang, Hing-Cheung So, Yuan Chen 0003, Wen-Qin Wang   +3 more
openaire   +2 more sources

Tensor Nuclear Norm LPV Subspace Identification

IEEE Transactions on Automatic Control, 2018
Linear 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, Jan-Willem van Wingerden, Michel Verhaegen   +2 more
openaire   +1 more source

Further results on tensor nuclear norms

Calcolo, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

A Mixture of Nuclear Norm and Matrix Factorization for Tensor Completion

Journal of Scientific Computing, 2017
The core problem of tensor completion is to estimate missing data via known data; for example, from \(3\)-dimensional scans. Let \(\mathcal{X}\) be a real \(N\)-mode tensor of size \(\ell_{1}\times\ell_{2}\times\cdots \times\ell_{N}\) with entries \(x_{i_{1}i_{2}\dots i_{N}}\) where the index \(i_{k}\) runs over a set \(I_{k}\) of size \(\ell_{k ...
Shangqi Gao, Qibin Fan
openaire   +1 more source

Fast Guaranteed Tensor Recovery with Adaptive Tensor Nuclear Norm

Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence
Real-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, Hailin Wang 0001, Xiangyong Cao, Shuang Xu   +3 more
openaire   +1 more source

Dynamic MRI Reconstruction Combining Tensor Nuclear Norm and Casorati Matrix Nuclear Norm

ISMRM Annual Meeting, 2023
Low-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 ...
Zhang, Yinghao, Hu, Yue, Lu, Xin
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Nuclear norm minimization and tensor completion in exploration seismology

2013 IEEE International Conference on Acoustics, Speech and Signal Processing, 2013
We consider the problem of multidimensional seismic data signal recovery and noise attenuation. These data are multi-dimensional signals that can be described via a low-rank fourth-order tensor in the frequency-space domain. Tensor completion strategies can be used to recover unrecorded observations and to improve the signal-to-noise ratio of seismic ...
Nadia Kreimer, Mauricio D. Sacchi
openaire   +2 more sources

Sparse and Truncated Nuclear Norm Based Tensor Completion

Neural Processing Letters, 2016
One of the main difficulties in tensor completion is the calculation of the tensor rank. Recently a tensor nuclear norm, which is equal to the weighted sum of matrix nuclear norms of all unfoldings of the tensor, was proposed to address this issue. However, in this approach, all the singular values are minimized simultaneously.
Zi-Fa Han, Chi-Sing Leung, Long-Ting Huang, Hing-Cheung So   +3 more
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Balanced Unfolding Induced Tensor Nuclear Norms for High-Order Tensor Completion

IEEE Transactions on Neural Networks and Learning Systems
The recently proposed tensor tubal rank has been witnessed to obtain extraordinary success in real-world tensor data completion. However, existing works usually fix the transform orientation along the third mode and may fail to turn multidimensional low-tubal-rank structure into account.
Yuning Qiu, Guoxu Zhou, Andong Wang, Qibin Zhao, Shengli Xie   +4 more
openaire   +3 more sources