mlsanityData to 7 Oct 2026

Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra

arXiv 2308.02621 ↗First posted 4 Aug 2023cs.CV cs.LGcited by 0

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Abstract (arXiv)

To improve the accuracy of color image completion with missing entries, we present a recovery method based on generalized higher-order scalars. We extend the traditional second-order matrix model to a more comprehensive higher-order matrix equivalent, called the "t-matrix" model, which incorporates a pixel neighborhood expansion strategy to characterize the local pixel constraints. This "t-matrix" model is then used to extend some commonly used matrix and tensor completion algorithms to their higher-order versions. We perform extensive experiments on various algorithms using simulated data and algorithms on simulated data and publicly available images and compare their performance. The results show that our generalized matrix completion model and the corresponding algorithm compare favorably with their lower-order tensor and conventional matrix counterparts.

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14 of 35 references.

References · 14

  1. 2018Tensor Robust Principal Component Analysis with A New Tensor Nuclear Normcited by 110
  2. 2019Nonparametric Regression on Low-Dimensional Manifolds using Deep ReLU Networks : Function Approximation and Statistical Recoverycited by 73
  3. 2014Novel methods for multilinear data completion and de-noising based on tensor-SVDcited by 56
  4. 2017Tensor Completion Algorithms in Big Data Analyticscited by 48
  5. 2021Data-driven discovery of intrinsic dynamicscited by 45
  6. 2018Exact Low Tubal Rank Tensor Recovery from Gaussian Measurementscited by 16
  7. 2017Low-Rank Tensor Completion by Truncated Nuclear Norm Regularizationcited by 7
  8. 2022A Survey on Hyperspectral Image Restoration: From the View of Low-Rank Tensor Approximationcited by 7
  9. 2021Beyond the Signs: Nonparametric Tensor Completion via Sign Seriescited by 4
  10. 2022Tensor Completion with Provable Consistency and Fairness Guarantees for Recommender Systemscited by 4
  11. 2020Generalized Visual Information Analysis via Tensorial Algebracited by 3
  12. 2020General Data Analytics with Applications to Visual Information Analysis: A Provable Backward-Compatible Semisimple Paradigm over T-Algebracited by 3
2 more
  1. 2022Tensor factorization based method for low rank matrix completion and its application on tensor completioncited by 2
  2. 2022Approximation of Images via Generalized Higher Order Singular Value Decomposition over Finite-dimensional Commutative Semisimple Algebracited by 1

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