mlsanityData to 14 Oct 2026

To Fold or Not to Fold: Graph Regularized Tensor Train for Visual Data Completion

arXiv 2306.11123 ↗First posted 19 Jun 2023eess.SP cs.CVcited by 3

Not on the map. Why?

Abstract (arXiv)

Tensor train (TT) representation has achieved tremendous success in visual data completion tasks, especially when it is combined with tensor folding. However, folding an image or video tensor breaks the original data structure, leading to local information loss as nearby pixels may be assigned into different dimensions and become far away from each other. In this paper, to fully preserve the local information of the original visual data, we explore not folding the data tensor, and at the same time adopt graph information to regularize local similarity between nearby entries. To overcome the high computational complexity introduced by the graph-based regularization in the TT completion problem, we propose to break the original problem into multiple sub-problems with respect to each TT core fiber, instead of each TT core as in traditional methods. Furthermore, to avoid heavy parameter tuning, a sparsity promoting probabilistic model is built based on the generalized inverse Gaussian (GIG) prior, and an inference algorithm is derived under the mean-field approximation. Experiments on both synthetic data and real-world visual data show the superiority of the proposed methods.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 21 of its 65 references that are in the map. First posted on arXiv 19 Jun 2023.

Builds on

21 of 65 references.

References · 21

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9 more
  1. 2018Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trainscited by 14
  2. 2015Fast Robust PCA on Graphscited by 13
  3. 2020Optimal High-order Tensor SVD via Tensor-Train Orthogonal Iterationcited by 11
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Neural Operator-Grounded Continuous Tensor Function Representation and Its Applicationscited by 0
  2. 2026Tensor Decomposition Structure Search Framework from an Interaction Perspectivecited by 0
  3. 2026Pre-Trained Low-Rank Tensor Decomposition for Multi-Dimensional Image Recoverycited by 0