mlsanityData to 7 Oct 2026

Novel methods for multilinear data completion and de-noising based on tensor-SVD

arXiv 1407.1785 ↗First posted 7 Jul 2014cs.CVcited by 56

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Abstract (arXiv)

In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, the notion of multilinear rank and a related tensor nuclear norm was proposed in [11] to characterize informational and structural complexity of multilinear data. We first show that videos with linear camera motion can be represented more efficiently using t-SVD compared to the approaches based on vectorizing or flattening of the tensors. Since efficiency in representation implies efficiency in recovery, we outline a tensor nuclear norm penalized algorithm for video completion from missing entries. Application of the proposed algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. We also consider the problem of tensor robust Principal Component Analysis (PCA) for de-noising 3-D video data from sparse random corruptions. We show superior performance of our method compared to the matrix robust PCA adapted to this setting as proposed in [4].

Key facts. Cited by 56 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Jul 2014.

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Citing papers per year: 2021: 10; 2022: 10; 2023: 14; 2024: 10; 2025: 10; 2026: 2.

56 papers.

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  1. 2022Low-Rank Tensor Function Representation for Multi-Dimensional Data Recoverycited by 45
  2. 2023DDS2M: Self-Supervised Denoising Diffusion Spatio-Spectral Model for Hyperspectral Image Restorationcited by 32
  3. 2021Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurementscited by 28
  4. 2021Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recoverycited by 16
  5. 2021Nonlinear Transform Induced Tensor Nuclear Norm for Tensor Completioncited by 13
  6. 2023Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruptioncited by 11
  7. 2022Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Reviewcited by 9
  8. 2021Fast Robust Tensor Principal Component Analysis via Fiber CUR Decompositioncited by 8
  9. 2022Tensor Recovery Based on A Novel Non-convex Function Minimax Logarithmic Concave Penalty Functioncited by 7
  10. 2023A Comparison of Image Denoising Methodscited by 7
  11. 2021Efficient Tensor Robust PCA under Hybrid Model of Tucker and Tensor Traincited by 6
  12. 2022Smooth Robust Tensor Completion for Background/Foreground Separation with Missing Pixels: Novel Algorithm with Convergence Guaranteecited by 5
38 more
  1. 2024OTLRM: Orthogonal Learning-based Low-Rank Metric for Multi-Dimensional Inverse Problemscited by 5
  2. 2021Non-Convex Tensor Low-Rank Approximation for Infrared Small Target Detectioncited by 4
  3. 2022Robust Implementation of Foreground Extraction and Vessel Segmentation for X-ray Coronary Angiography Image Sequencecited by 4
  4. 2024Image Denoising Using Green Channel Priorcited by 4
  5. 2021Temporal Network Embedding via Tensor Factorizationcited by 3
  6. 2023Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizerscited by 3
  7. 2024Irregular Tensor Low-Rank Representation for Hyperspectral Image Representationcited by 3
  8. 2022Bayesian Robust Tensor Ring Model for Incomplete Multiway Datacited by 2
  9. 2023Handling The Non-Smooth Challenge in Tensor SVD: A Multi-Objective Tensor Recovery Frameworkcited by 2
  10. 2024Optimal Matrix-Mimetic Tensor Algebras via Variable Projectioncited by 2
  11. 2025Learnable Scaled Gradient Descent for Guaranteed Robust Tensor PCAcited by 2
  12. 2021Two New Low Rank Tensor Completion Methods Based on Sum Nuclear Normcited by 1
  13. 2022Tensor Factorization via Transformed Tensor-Tensor Product for Image Alignmentcited by 1
  14. 2023Non-convex approaches for low-rank tensor completion under tubal samplingcited by 1
  15. 2023A Novel Tensor Factorization-Based Method with Robustness to Inaccurate Rank Estimationcited by 1
  16. 2023T-ADAF: Adaptive Data Augmentation Framework for Image Classification Network based on Tensor T-product Operatorcited by 1
  17. 2023Low-rank tensor completion via tensor joint rank with logarithmic composite normcited by 1
  18. 2024Coseparable Nonnegative Tensor Factorization With T-CUR Decompositioncited by 1
  19. 2024Color Image Denoising Using The Green Channel Priorcited by 1
  20. 2024DTR: A Unified Deep Tensor Representation Framework for Multimedia Data Recoverycited by 1
  21. 2024Broadcast Product: Redefining Shape-aligned Element-wise Multiplication and Beyondcited by 1
  22. 2025Efficient Differentiable Approximation of Generalized Low-rank Regularizationcited by 1
  23. 2025Gaussian Splatting-based Low-Rank Tensor Representation for Multi-Dimensional Image Recoverycited by 1
  24. 2021Convolutional Graph-Tensor Net for Graph Data Completioncited by 0
  25. 2021Tensor Full Feature Measure and Its Nonconvex Relaxation Applications to Tensor Recoverycited by 0
  26. 2022Low-Rank Tensor Completion Based on Bivariate Equivalent Minimax-Concave Penaltycited by 0
  27. 2022Multi-mode Tensor Train Factorization with Spatial-spectral Regularization for Remote Sensing Images Recoverycited by 0
  28. 2022Highlight Specular Reflection Separation based on Tensor Low-rank and Sparse Decomposition Using Polarimetric Cuescited by 0
  29. 2023High-dimensional multi-view clustering methodscited by 0
  30. 2023Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebracited by 0
  31. 2023Tensor Completion Leveraging Graph Information: A Dynamic Regularization Approach with Statistical Guaranteescited by 0
  32. 2023Infrared Small Target Detection Using Double-Weighted Multi-Granularity Patch Tensor Model With Tensor-Train Decompositioncited by 0
  33. 2023Low-Multi-Rank High-Order Bayesian Robust Tensor Factorizationcited by 0
  34. 2024A PID-Controlled Non-Negative Tensor Factorization Model for Analyzing Missing Data in NILMcited by 0
  35. 2024Projected Tensor-Tensor Products for Efficient Computation of Optimal Multiway Data Representationscited by 0
  36. 2025Triply Laplacian Scale Mixture Modeling for Seismic Data Noise Suppressioncited by 0
  37. 2025A novel non-convex minimax p-th order concave penalty function approach to low-rank tensor completioncited by 0
  38. 2025Quantile-Based Randomized Kaczmarz for Corrupted Tensor Linear Systemscited by 0

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