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Related papers: Low-M-Rank Tensor Completion and Robust Tensor PCA

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In recent years, low-rank tensor completion (LRTC) has received considerable attention due to its applications in image/video inpainting, hyperspectral data recovery, etc. With different notions of tensor rank (e.g., CP, Tucker, tensor…

Machine Learning · Statistics 2020-10-30 Yunfeng Cai , Ping Li

Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…

Statistics Theory · Mathematics 2016-09-14 Anil Aswani

The problem of recovering a low $n$-rank tensor is an extension of sparse recovery problem from the low dimensional space (matrix space) to the high dimensional space (tensor space) and has many applications in computer vision and graphics…

Optimization and Control · Mathematics 2014-04-09 Min Zhang , Lei Yang , Zheng-Hai Huang

The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low-tubal-rank was shown to give a valuable characterization…

Machine Learning · Computer Science 2022-10-18 Yicong He , George K. Atia

Low-rank tensor recovery has attracted much attention among various tensor recovery approaches. A tensor rank has several definitions, unlike the matrix rank--e.g. the CP rank and the Tucker rank. Many low-rank tensor recovery methods are…

Signal Processing · Electrical Eng. & Systems 2020-09-09 Kaito Hosono , Shunsuke Ono , Takamichi Miyata

In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…

Numerical Analysis · Computer Science 2018-05-23 Longhao Yuan , Chao Li , Danilo Mandic , Jianting Cao , Qibin Zhao

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks…

Numerical Analysis · Computer Science 2017-04-26 Johann A. Bengua , Ho N. Phien , Hoang D. Tuan , Minh N. Do

Dimension reduction techniques are often used when the high-dimensional tensor has relatively low intrinsic rank compared to the ambient dimension of the tensor. The CANDECOMP/PARAFAC (CP) tensor completion is a widely used approach to find…

Numerical Analysis · Mathematics 2021-04-01 Jiahua Jiang , Fatoumata Sanogo , Carmeliza Navasca

Tensor completion is a challenging problem with various applications. Many related models based on the low-rank prior of the tensor have been proposed. However, the low-rank prior may not be enough to recover the original tensor from the…

Numerical Analysis · Mathematics 2019-11-20 Ping-Ping Wang , Liang Li , Guang-Hui Cheng

We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each…

Optimization and Control · Mathematics 2020-07-28 Dong-Hui Li , Cui-Dan Chen , Hong-Bo Guan

We consider a novel algorithm, for the completion of partially observed low-rank tensors, where each entry of the tensor can be chosen from a discrete finite alphabet set, such as in common image processing problems, where the entries…

Signal Processing · Electrical Eng. & Systems 2026-02-06 Niclas Führling , Getuar Rexhepi , Giuseppe Abreu

Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…

Machine Learning · Computer Science 2021-05-21 Chenjian Pan , Chen Ling , Hongjin He , Liqun Qi , Yanwei Xu

Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…

Optimization and Control · Mathematics 2024-08-23 Quan Yu , Xinzhen Zhang

This paper studies the Tensor Robust Principal Component (TRPCA) problem which extends the known Robust PCA (Candes et al. 2011) to the tensor case. Our model is based on a new tensor Singular Value Decomposition (t-SVD) (Kilmer and Martin…

Computer Vision and Pattern Recognition · Computer Science 2018-05-29 Canyi Lu , Jiashi Feng , Yudong Chen , Wei Liu , Zhouchen Lin , Shuicheng Yan

The low-rank tensor completion (LRTC) problem aims to reconstruct a tensor from partial sample information, which has attracted significant interest in a wide range of practical applications such as image processing and computer vision.…

Computer Vision and Pattern Recognition · Computer Science 2025-06-09 Hongbing Zhang , Bing Zheng

Low-rank tensor completion (LRTC) is an important problem in computer vision and machine learning. The minimax-concave penalty (MCP) function as a non-convex relaxation has achieved good results in the LRTC problem. To makes all the…

Computer Vision and Pattern Recognition · Computer Science 2022-09-20 Hongbing Zhang , Xinyi Liu , Hongtao Fan , Yajing Li , Yinlin Ye

New-generation wireless communication systems will employ large-scale antenna arrays to satisfy the increasing capacity demand. This massive scenario brings new challenges to the channel equalization problem due to the increased signal…

Signal Processing · Electrical Eng. & Systems 2019-12-19 Lucas N. Ribeiro , André L. F. de Almeida , João C. M. Mota

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

Statistics Theory · Mathematics 2021-02-08 Rungang Han , Rebecca Willett , Anru R. Zhang

The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…

Numerical Analysis · Mathematics 2021-04-13 Liyu Su

Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…

Numerical Analysis · Mathematics 2021-01-03 Abdul Ahad , Zhen Long , Ce Zhu , Yipeng Liu