# Multi-Dimensional Visual Data Recovery: Scale-Aware Tensor Modeling and Accelerated Randomized Computation

arXiv: https://arxiv.org/abs/2602.12982 · HTML: https://mlsanity.com/paper/2602.12982/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 88 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Builds on (most cited first, 22 of 22)

- [HyperSIGMA: Hyperspectral Intelligence Comprehension Foundation Model](https://mlsanity.com/paper/2406.11519/) (2024)
- [Efficient tensor completion for color image and video recovery: Low-rank tensor train](https://mlsanity.com/paper/1606.01500/) (2016)
- [Tensor Completion Algorithms in Big Data Analytics](https://mlsanity.com/paper/1711.10105/) (2017)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion](https://mlsanity.com/paper/1809.02288/) (2018)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [An Optimal Statistical and Computational Framework for Generalized Tensor Estimation](https://mlsanity.com/paper/2002.11255/) (2020)
- [Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery](https://mlsanity.com/paper/1307.5870/) (2013)
- [Robust Low-rank Tensor Recovery: Models and Algorithms](https://mlsanity.com/paper/1311.6182/) (2013)
- [Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurements](https://mlsanity.com/paper/2104.14526/) (2021)
- [A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems](https://mlsanity.com/paper/1303.4434/) (2013)
- [Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization](https://mlsanity.com/paper/2103.08895/) (2021)
- [Tensor N-tubal rank and its convex relaxation for low-rank tensor recovery](https://mlsanity.com/paper/1812.00688/) (2018)
- [High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantization](https://mlsanity.com/paper/2202.13157/) (2022)
- [Tensor-Ring Nuclear Norm Minimization and Application for Visual Data Completion](https://mlsanity.com/paper/1903.08888/) (2019)
- [Guaranteed Nonconvex Factorization Approach for Tensor Train Recovery](https://mlsanity.com/paper/2401.02592/) (2024)
- [Tensor Recovery Based on A Novel Non-convex Function Minimax Logarithmic Concave Penalty Function](https://mlsanity.com/paper/2206.13506/) (2022)
- [Low-Tubal-Rank Tensor Recovery via Factorized Gradient Descent](https://mlsanity.com/paper/2401.11940/) (2024)
- [Fully-Connected Tensor Network Decomposition for Robust Tensor Completion Problem](https://mlsanity.com/paper/2110.08754/) (2021)
- [Quantized Low-Rank Multivariate Regression with Random Dithering](https://mlsanity.com/paper/2302.11197/) (2023)
- [Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizers](https://mlsanity.com/paper/2310.06233/) (2023)
- [Hyperspectral Anomaly Detection Fused Unified Nonconvex Tensor Ring Factors Regularization](https://mlsanity.com/paper/2505.17881/) (2025)

## Abstract (arXiv)

The recently proposed fully-connected tensor network (FCTN) decomposition has demonstrated significant advantages in correlation characterization and transpositional invariance, and has achieved notable achievements in multi-dimensional data processing and analysis. However, existing multi-dimensional data recovery methods leveraging FCTN decomposition still have room for further enhancement, particularly in computational efficiency and modeling capability. To address these issues, we first propose a FCTN-based generalized nonconvex regularization paradigm from the perspective of gradient mapping. Then, reliable and scalable multi-dimensional data recovery models are investigated, where the model formulation is shifted from unquantized observations to coarse-grained quantized observations. Based on the alternating direction method of multipliers (ADMM) framework, we derive efficient optimization algorithms with convergence guarantees to solve the formulated models. To alleviate the computational bottleneck encountered when processing large-scale multi-dimensional data, fast and efficient randomized compression algorithms are devised in virtue of sketching techniques in numerical linear algebra. These dimensionality-reduction techniques serve as the computational acceleration core of our proposed algorithm framework. Theoretical results on approximation error upper bounds and convergence analysis for the proposed method are derived. Extensive numerical experiments illustrate the effectiveness and superiority of the proposed algorithm over other state-of-the-art methods in terms of quantitative metrics, visual quality, and running time.