mlsanityData to 7 Oct 2026

Efficient tensor completion for color image and video recovery: Low-rank tensor train

arXiv 1606.01500 ↗First posted 5 Jun 2016math.NA cs.DS cs.NAcited by 61

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Abstract (arXiv)

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 to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor train (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via tensor train (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher-orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

Key facts. Cited by 61 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Jun 2016.

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Citing papers per year: 2021: 10; 2022: 13; 2023: 13; 2024: 4; 2025: 12; 2026: 9.

61 papers.

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  1. 2022Low-Rank Tensor Function Representation for Multi-Dimensional Data Recoverycited by 45
  2. 2023Guaranteed Tensor Recovery Fused Low-rankness and Smoothnesscited by 41
  3. 2023DDS2M: Self-Supervised Denoising Diffusion Spatio-Spectral Model for Hyperspectral Image Restorationcited by 32
  4. 2021Provable Tensor-Train Format Tensor Completion by Riemannian Optimizationcited by 17
  5. 2021Nonlinear Transform Induced Tensor Nuclear Norm for Tensor Completioncited by 13
  6. 2022Noisy Tensor Completion via Low-rank Tensor Ringcited by 13
  7. 2022Permutation Search of Tensor Network Structures via Local Samplingcited by 13
  8. 2022Rethinking Bayesian Learning for Data Analysis: The Art of Prior and Inference in Sparsity-Aware Modelingcited by 12
  9. 2023SVDinsTN: A Tensor Network Paradigm for Efficient Structure Search from Regularized Modeling Perspectivecited by 9
  10. 2021Effective Tensor Completion via Element-wise Weighted Low-rank Tensor Train with Overlapping Ket Augmentationcited by 8
  11. 2024Guaranteed Nonconvex Factorization Approach for Tensor Train Recoverycited by 8
  12. 2023A Comparison of Image Denoising Methodscited by 7
38 more
  1. 2023Multi-view MERA Subspace Clusteringcited by 7
  2. 2023Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximationcited by 7
  3. 2024Low-Tubal-Rank Tensor Recovery via Factorized Gradient Descentcited by 7
  4. 2021Nonlocal Patch-Based Fully-Connected Tensor Network Decomposition for Remote Sensing Image Inpaintingcited by 6
  5. 2021Tensor train completion: local recovery guarantees via Riemannian optimizationcited by 6
  6. 2021Efficient Tensor Robust PCA under Hybrid Model of Tucker and Tensor Traincited by 6
  7. 2021Fully-Connected Tensor Network Decomposition for Robust Tensor Completion Problemcited by 5
  8. 2022Connections between Deep Equilibrium and Sparse Representation Models with Application to Hyperspectral Image Denoisingcited by 4
  9. 2023Adaptively Topological Tensor Network for Multi-view Subspace Clusteringcited by 4
  10. 2021Coarse to Fine Two-Stage Approach to Robust Tensor Completion of Visual Datacited by 3
  11. 2022Many-body Approximation for Non-negative Tensorscited by 3
  12. 2023To Fold or Not to Fold: Graph Regularized Tensor Train for Visual Data Completioncited by 3
  13. 2023Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizerscited by 3
  14. 2021Patch Tracking-based Streaming Tensor Ring Completion for Visual Data Recoverycited by 2
  15. 2022Bayesian Robust Tensor Ring Model for Incomplete Multiway Datacited by 2
  16. 2024Sharp Analysis of Power Iteration for Tensor PCAcited by 2
  17. 2026Calibrated Harmonic Overlaid Implicit Neural Representations for Multi-Dimensional Datacited by 2
  18. 2022Low-rank Tensor Learning with Nonconvex Overlapped Nuclear Norm Regularizationcited by 1
  19. 2022Variational Bayesian inference for CP tensor completion with side informationcited by 1
  20. 2022Error Analysis of Tensor-Train Cross Approximationcited by 1
  21. 2024Low-Rank Tensor Learning by Generalized Nonconvex Regularizationcited by 1
  22. 2025Tensor Train Completion from Fiberwise Observations Along a Single Modecited by 1
  23. 2025Gaussian Splatting-based Low-Rank Tensor Representation for Multi-Dimensional Image Recoverycited by 1
  24. 2021"Sparse + Low-Rank'' Tensor Completion Approach for Recovering Images and Videoscited by 0
  25. 2022Multi-mode Tensor Train Factorization with Spatial-spectral Regularization for Remote Sensing Images Recoverycited by 0
  26. 2022Latent Matrices for Tensor Network Decomposition and to Tensor Completioncited by 0
  27. 2022Tucker-O-Minus Decomposition for Multi-view Tensor Subspace Clusteringcited by 0
  28. 2023Optical Coherence Tomography Image Enhancement via Block Hankelization and Low Rank Tensor Network Approximationcited by 0
  29. 2023Quaternion tensor left ring decomposition and application for color image inpaintingcited by 0
  30. 2023Infrared Small Target Detection Using Double-Weighted Multi-Granularity Patch Tensor Model With Tensor-Train Decompositioncited by 0
  31. 2023Low-Multi-Rank High-Order Bayesian Robust Tensor Factorizationcited by 0
  32. 2025Fast and Provable Tensor-Train Format Tensor Completion via Precondtioned Riemannian Gradient Descentcited by 0
  33. 2025Under-Sampled High-Dimensional Data Recovery via Symbiotic Multi-Prior Tensor Reconstructioncited by 0
  34. 2025Accelerating Large-Scale Regularized High-Order Tensor Recoverycited by 0
  35. 2025Normalized Iterative Hard Thresholding for Tensor Recoverycited by 0
  36. 2025LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completioncited by 0
  37. 2025Efficient Image Denoising Using Global and Local Circulant Representationcited by 0
  38. 2025Superpixel-informed Continuous Low-Rank Tensor Representation for Multi-Dimensional Data Recoverycited by 0

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