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In recent studies, the tensor ring (TR) rank has shown high effectiveness in tensor completion due to its ability of capturing the intrinsic structure within high-order tensors. A recently proposed TR rank minimization method is based on…

Computer Vision and Pattern Recognition · Computer Science 2020-05-21 Meng Ding , Ting-Zhu Huang , Xi-Le Zhao , Tian-Hui Ma

This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…

Numerical Analysis · Mathematics 2025-09-01 Mohamed El Guide , Anas El Hachimi , Khalide Jbilou , Lothar Reichel

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

A tensor nuclear norm (TNN) based method for solving the tensor recovery problem was recently proposed, and it has achieved state-of-the-art performance. However, it may fail to produce a highly accurate solution since it tends to treats…

Optimization and Control · Mathematics 2022-05-13 Quan Yu

The robust low-rank tensor completion problem addresses the challenge of recovering corrupted high-dimensional tensor data with missing entries, outliers, and sparse noise commonly found in real-world applications. Existing methodologies…

Machine Learning · Statistics 2026-04-16 Biswarup Karmakar , Ratikanta Behera

We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…

Machine Learning · Statistics 2009-06-12 Rahul Mazumder , Trevor Hastie , Rob Tibshirani

Matrix completion focuses on recovering a matrix from a small subset of its observed elements, and has already gained cumulative attention in computer vision. Many previous approaches formulate this issue as a low-rank matrix approximation…

Computer Vision and Pattern Recognition · Computer Science 2019-01-08 Shengke Xue , Wenyuan Qiu , Fan Liu , Xinyu Jin

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

Recent approaches to the tensor completion problem have often overlooked the nonnegative structure of the data. We consider the problem of learning a nonnegative low-rank tensor, and using duality theory, we propose a novel factorization of…

Computer Vision and Pattern Recognition · Computer Science 2023-05-16 Tanmay Kumar Sinha , Jayadev Naram , Pawan Kumar

With the advancement of the data acquisition techniques, multi-view learning has become a hot topic. Some multi-view learning methods assume that the multi-view data is complete, which means that all instances are present, but this too…

Machine Learning · Computer Science 2022-08-09 Heng Zhang , Xiaohong Chen

In this paper, we consider the tensor completion problem, which has many researchers in the machine learning particularly concerned. Our fast and precise method is built on extending the $L_{2,1}$-norm minimization and Qatar Riyal…

Numerical Analysis · Mathematics 2020-11-10 Yongming Zheng , An-Bao Xu

Tensor completion recovers missing entries of multiway data. Teh missing of entries could often be caused during teh data acquisition and transformation. In dis paper, we provide an overview of recent development in low rank tensor…

Numerical Analysis · Computer Science 2018-05-11 Zhen Long , Yipeng Liu , Longxi Chen , Ce Zhu

The main challenge with the tensor completion problem is a fundamental tension between computation power and the information-theoretic sample complexity rate. Past approaches either achieve the information-theoretic rate but lack practical…

Optimization and Control · Mathematics 2024-04-05 Xin Chen , Sukanya Kudva , Yongzheng Dai , Anil Aswani , Chen Chen

The low-tubal-rank tensor model has been recently proposed for real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of its…

Machine Learning · Computer Science 2016-10-12 Xiao-Yang Liu , Shuchin Aeron , Vaneet Aggarwal , Xiaodong Wang

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…

Machine Learning · Computer Science 2019-07-10 Chunsheng Liu , Hong Shan , Chunlei Chen

Recently, a tensor factorization based method for a low tubal rank tensor completion problem of a third order tensor was proposed, which performed better than some existing methods. Tubal rank is only defined on one mode of third order…

Optimization and Control · Mathematics 2024-08-20 Quan Yu , Xinzhen Zhang , Zheng-Hai Huang

In our paper, we have studied the tensor completion problem when the sampling pattern is deterministic. We first propose a simple but efficient weighted HOSVD algorithm for recovery from noisy observations. Then we use the weighted HOSVD…

Numerical Analysis · Mathematics 2020-03-23 Zehan Chao , Longxiu Huang , Deanna Needell

In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…

Information Theory · Computer Science 2013-11-01 Zemin Zhang , Gregory Ely , Shuchin Aeron , Ning Hao , Misha Kilmer

Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…

Machine Learning · Statistics 2020-12-15 Chanwoo Lee , Miaoyan Wang

Low-rank quaternion tensor completion method, a novel approach to recovery color videos and images is proposed in this paper. We respectively reconstruct a color image and a color video as a quaternion matrix (second-order tensor) and a…

Numerical Analysis · Mathematics 2020-01-30 Jifei Miao , Kit Ian Kou , Wankai Liu