Journal Article10.1109/TSP.2021.3086363
A Novel Regularized Model for Third-Order Tensor Completion
19
TL;DR: In this paper, a tensor completion approach within the tensor singular value decomposition (t-svd) framework was proposed to solve the associated nonconvex tensor multi-rank minimization problem.
read more
Abstract: Inspired by the accuracy and efficiency of the $\gamma$ -norm of a matrix, which is closer to the original rank minimization problem than nuclear norm minimization (NNM), we generalize the $\gamma$ -norm of a matrix to tensors and propose a new tensor completion approach within the tensor singular value decomposition (t-svd) framework. An efficient algorithm, which combines the augmented Lagrange multiplier and closed-resolution of a cubic equation, was developed to solve the associated nonconvex tensor multi-rank minimization problem. Experimental results show that the proposed approach has an advantage over current state of the art algorithms in recovery accuracy.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns
Tong Nie,Guoyang Qin,Jian Sun +2 more
TL;DR: Wang et al. as discussed by the authors proposed an innovative nonconvex truncated Schatten p-norm for tensors (TSpN) to approximate tensor rank and impute missing spatio-temporal traffic data under the LRTC framework.
3-D Array Image Data Completion by Tensor Decomposition and Nonconvex Regularization Approach
TL;DR: In this paper , a new nonconvex regularization approach was proposed to better capture the low-rank characteristics than the convex approach, which can better solve the problem.
11
Robust low-rank tensor completion via new regularized model with approximate SVD
Fengsheng Wu,Chaoqian Li,Yaotang Li,Niansheng Tang +3 more
TL;DR: In this paper , a low-rank tensor completion model with the robust form was proposed by minimizing the reconstruction error of approximate SVD and the γ nuclear norm of the lower triangular tensor, and then give their equivalent forms with the tensor slices in the Fourier domain.
4
Spatiotemporal traffic data completion with truncated minimax-concave penalty
Peng Chen,Fang Li,Deliang Wei,Changhong Lu +3 more
2
Smooth Tensor Product for Tensor Completion
Tongle Wu,Jicong Fan +1 more
TL;DR: This paper introduces a novel tensor completion model that leverages global low-rank structure and local smoothness of factor tensors, proposing an efficient optimization method and establishing tighter generalization error bounds for improved recovery performance.
2
References
Image quality assessment: from error visibility to structural similarity
TL;DR: In this article, a structural similarity index is proposed for image quality assessment based on the degradation of structural information, which can be applied to both subjective ratings and objective methods on a database of images compressed with JPEG and JPEG2000.
•Book
Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers
Stephen Boyd,Neal Parikh,Eric Chu,Borja Peleato,Jonathan Eckstein +4 more
- 23 May 2011
TL;DR: It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.
Tensor Decompositions and Applications
Tamara G. Kolda,Brett W. Bader +1 more
TL;DR: This survey provides an overview of higher-order tensor decompositions, their applications, and available software.
Robust principal component analysis
TL;DR: In this paper, the authors prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the e1 norm.
A Singular Value Thresholding Algorithm for Matrix Completion
TL;DR: This paper develops a simple first-order and easy-to-implement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank, and develops a framework in which one can understand these algorithms in terms of well-known Lagrange multiplier algorithms.