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Quaternion tensor left ring decomposition and application for color image inpainting

arXiv 2307.10620 ↗First posted 20 Jul 2023cs.CV cs.NA math.NAcited by 0

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Abstract (arXiv)

In recent years, tensor networks have emerged as powerful tools for solving large-scale optimization problems. One of the most promising tensor networks is the tensor ring (TR) decomposition, which achieves circular dimensional permutation invariance in the model through the utilization of the trace operation and equitable treatment of the latent cores. On the other hand, more recently, quaternions have gained significant attention and have been widely utilized in color image processing tasks due to their effectiveness in encoding color pixels by considering the three color channels as a unified entity. Therefore, in this paper, based on the left quaternion matrix multiplication, we propose the quaternion tensor left ring (QTLR) decomposition, which inherits the powerful and generalized representation abilities of the TR decomposition while leveraging the advantages of quaternions for color pixel representation. In addition to providing the definition of QTLR decomposition and an algorithm for learning the QTLR format, the paper further proposes a low-rank quaternion tensor completion (LRQTC) model and its algorithm for color image inpainting based on the defined QTLR decomposition. Finally, extensive experiments on color image inpainting demonstrate that the proposed LRQTC method is highly competitive.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 15 of its 52 references that are in the map. First posted on arXiv 20 Jul 2023.

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References · 15

  1. 2016Tensor Ring Decompositioncited by 125
  2. 2015Exact tensor completion using t-SVDcited by 70
  3. 2016Efficient tensor completion for color image and video recovery: Low-rank tensor traincited by 61
  4. 2017Efficient Low Rank Tensor Ring Completioncited by 45
  5. 2018Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completioncited by 42
  6. 2019Color image recovery using low-rank quaternion matrix completion algorithmcited by 14
  7. 2022Noisy Tensor Completion via Low-rank Tensor Ringcited by 13
  8. 2019Tensor-Ring Nuclear Norm Minimization and Application for Visual Data Completioncited by 12
  9. 2020Quaternion-based bilinear factor matrix norm minimization for color image inpaintingcited by 12
  10. 2019Provable Tensor Ring Completioncited by 8
  11. 2021Effective Tensor Completion via Element-wise Weighted Low-rank Tensor Train with Overlapping Ket Augmentationcited by 8
  12. 2022Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Losscited by 8
3 more
  1. 2023Quaternion Matrix Completion Using Untrained Quaternion Convolutional Neural Network for Color Image Inpaintingcited by 4
  2. 2020A Low Rank Quaternion Decomposition Algorithm and Its Application in Color Image Inpaintingcited by 3
  3. 2022Quaternion Tensor Train Rank Minimization with Sparse Regularization in a Transformed Domain for Quaternion Tensor Completioncited by 1

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