mlsanityData to 7 Oct 2026

Guaranteed Tensor Recovery Fused Low-rankness and Smoothness

arXiv 2302.02155 ↗First posted 4 Feb 2023cs.LG cs.AI cs.CVcited by 41

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Abstract (arXiv)

The tensor data recovery task has thus attracted much research attention in recent years. Solving such an ill-posed problem generally requires to explore intrinsic prior structures underlying tensor data, and formulate them as certain forms of regularization terms for guiding a sound estimate of the restored tensor. Recent research have made significant progress by adopting two insightful tensor priors, i.e., global low-rankness (L) and local smoothness (S) across different tensor modes, which are always encoded as a sum of two separate regularization terms into the recovery models. However, unlike the primary theoretical developments on low-rank tensor recovery, these joint L+S models have no theoretical exact-recovery guarantees yet, making the methods lack reliability in real practice. To this crucial issue, in this work, we build a unique regularization term, which essentially encodes both L and S priors of a tensor simultaneously. Especially, by equipping this single regularizer into the recovery models, we can rigorously prove the exact recovery guarantees for two typical tensor recovery tasks, i.e., tensor completion (TC) and tensor robust principal component analysis (TRPCA). To the best of our knowledge, this should be the first exact-recovery results among all related L+S methods for tensor recovery. Significant recovery accuracy improvements over many other SOTA methods in several TC and TRPCA tasks with various kinds of visual tensor data are observed in extensive experiments. Typically, our method achieves a workable performance when the missing rate is extremely large, e.g., 99.5%, for the color image inpainting task, while all its peers totally fail in such challenging case.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). Builds on 24 of its 85 references that are in the map. First posted on arXiv 4 Feb 2023.

Builds on

24 of 85 references.

References · 24

  1. 2016Tensor Ring Decompositioncited by 125
  2. 2018Tensor Robust Principal Component Analysis with A New Tensor Nuclear Normcited by 110
  3. 2015Exact tensor completion using t-SVDcited by 70
  4. 2014Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determinationcited by 65
  5. 2016Efficient tensor completion for color image and video recovery: Low-rank tensor traincited by 61
  6. 2017Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decompositioncited by 61
  7. 2021Tensor Methods in Computer Vision and Deep Learningcited by 52
  8. 2017Efficient Low Rank Tensor Ring Completioncited by 45
  9. 2013Square Deal: Lower Bounds and Improved Relaxations for Tensor Recoverycited by 37
  10. 2015Smooth PARAFAC Decomposition for Tensor Completioncited by 34
  11. 2013Robust Low-rank Tensor Recovery: Models and Algorithmscited by 33
  12. 2013Tensor-based formulation and nuclear norm regularization for multi-energy computed tomographycited by 22
12 more
  1. 2014Bayesian Robust Tensor Factorization for Incomplete Multiway Datacited by 22
  2. 2022Exact Decomposition of Joint Low Rankness and Local Smoothness Plus Sparse Matricescited by 19
  3. 2016Low-tubal-rank Tensor Completion using Alternating Minimizationcited by 18
  4. 2018Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trainscited by 14
  5. 2022Fast Noise Removal in Hyperspectral Images via Representative Coefficient Total Variationcited by 13
  6. 2017Large-Scale Low-Rank Matrix Learning with Nonconvex Regularizerscited by 10
  7. 2013A New Convex Relaxation for Tensor Completioncited by 9
  8. 2013Convex Tensor Decomposition via Structured Schatten Norm Regularizationcited by 8
  9. 2015Collaborative Total Variation: A General Framework for Vectorial TV Modelscited by 5
  10. 2015Tensor vs Matrix Methods: Robust Tensor Decomposition under Block Sparse Perturbationscited by 5
  11. 2013Guarantees of Total Variation Minimization for Signal Recoverycited by 3
  12. 2020Projected Robust PCA with Application to Smooth Image Recoverycited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 8; 2025: 21; 2026: 10.

41 papers.

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  1. 2024Revisiting Nonlocal Self-Similarity from Continuous Representationcited by 14
  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. 2024NeurTV: Total Variation on the Neural Domaincited by 7
  5. 2024Pan-denoising: Guided Hyperspectral Image Denoising via Weighted Represent Coefficient Total Variationcited by 4
  6. 2024Hipandas: Hyperspectral Image Joint Denoising and Super-Resolution by Image Fusion with the Panchromatic Imagecited by 3
  7. 2025Learnable Scaled Gradient Descent for Guaranteed Robust Tensor PCAcited by 2
  8. 2025Guaranteed Multidimensional Time Series Prediction via Deterministic Tensor Completion Theorycited by 2
  9. 2025Cross-Frequency Implicit Neural Representation with Self-Evolving Parameterscited by 2
  10. 2025Hyperspectral Anomaly Detection Fused Unified Nonconvex Tensor Ring Factors Regularizationcited by 2
  11. 2025It's Not the Target, It's the Background: Rethinking Infrared Small Target Detection via Deep Patch-Free Low-Rank Representationscited by 2
  12. 2024Power of ℓ1-Norm Regularized Kaczmarz Algorithms for High-Order Tensor Recoverycited by 1
29 more
  1. 2024Haar Nuclear Norms with Applications to Remote Sensing Imagery Restorationcited by 1
  2. 2025Low-Rank Tensor Recovery via Variational Schatten-p Quasi-Norm and Jacobian Regularizationcited by 1
  3. 2025Beyond Motion Cues and Structural Sparsity: Revisiting Small Moving Target Detectioncited by 1
  4. 2025Gaussian Splatting-based Low-Rank Tensor Representation for Multi-Dimensional Image Recoverycited by 1
  5. 2023Neural Gradient Regularizercited by 0
  6. 2024Variational Bayesian Inference for Tensor Robust Principal Component Analysiscited by 0
  7. 2025Outlier-aware Tensor Robust Principal Component Analysis with Self-guided Data Augmentationcited by 0
  8. 2025Accelerating Large-Scale Regularized High-Order Tensor Recoverycited by 0
  9. 20253DeepRep: 3D Deep Low-rank Tensor Representation for Hyperspectral Image Inpaintingcited by 0
  10. 2025Robust Tensor Completion via Gradient Tensor Nulclear L1-L2 Norm for Traffic Data Recoverycited by 0
  11. 2025Beyond Low-rankness: Guaranteed Matrix Recovery via Modified Nuclear Normcited by 0
  12. 2025Hyperspectral Image Recovery Constrained by Multi-Granularity Non-Local Self-Similarity Priorscited by 0
  13. 2025LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completioncited by 0
  14. 2025Superpixel-informed Continuous Low-Rank Tensor Representation for Multi-Dimensional Data Recoverycited by 0
  15. 2025Generalized Nonnegative Structured Kruskal Tensor Regressioncited by 0
  16. 2025Compact Multi-level-prior Tensor Representation for Hyperspectral Image Super-resolutioncited by 0
  17. 2025Tensor Completion via Monotone Inclusion: Generalized Low-Rank Priors Meet Deep Denoiserscited by 0
  18. 2025An Interdisciplinary and Cross-Task Review on Missing Data Imputationcited by 0
  19. 2025Exact Recovery of Non-Random Missing Multidimensional Time Series via Temporal Isometric Delay-Embedding Transformcited by 0
  20. 2026Multi-Dimensional Visual Data Recovery: Scale-Aware Tensor Modeling and Accelerated Randomized Computationcited by 0
  21. 2026Nonconvex Latent Optimally Partitioned Block-Sparse Recovery via Log-Sum and Minimax Concave Penaltiescited by 0
  22. 2026Neural Operator-Grounded Continuous Tensor Function Representation and Its Applicationscited by 0
  23. 2026Robust Principal Component Completioncited by 0
  24. 2026Robust Low-Rank Tensor Completion based on M-product with Weighted Correlated Total Variation and Sparse Regularizationcited by 0
  25. 2026Robust Tensor Regression with Nonconvexity: Algorithmic and Statistical Theorycited by 0
  26. 2026Bayesian Tensor Decomposition with Diffusion Model Priorcited by 0
  27. 2026Exponential-Family Tensor Completion via Nonconvex Dual Total-Variation Regularizationcited by 0
  28. 2026Semi-Tensor Product-Based Multi-Term Randomized T-SVD and Its Visual Applicationscited by 0
  29. 2026Pre-Trained Low-Rank Tensor Decomposition for Multi-Dimensional Image Recoverycited by 0