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

• URL: http://arxiv.org/abs/2602.12982v1
• Date: Fri, 13 Feb 2026 14:56:37 GMT
• Title: Multi-Dimensional Visual Data Recovery: Scale-Aware Tensor Modeling and Accelerated Randomized Computation
• Authors: Wenjin Qin, Hailin Wang, Jiangjun Peng, Jianjun Wang, Tingwen Huang,
• Abstract summary: We propose a new type of network compression optimization technique, fully randomized tensor network compression (FCTN)<n>FCTN has significant advantages in correlation characterization and transpositional in algebra, and has notable achievements in multi-dimensional data processing and analysis.<n>We derive efficient algorithms with guarantees to solve the formulated models.
• Score: 51.65236537605077
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Neural Optimal Transport Meets Multivariate Conformal Prediction [58.43397908730771]
  We propose a framework for conditional vectorile regression (CVQR)<n>CVQR combines neural optimal transport with quantized optimization, and apply it to predictions.
  arXiv  Detail & Related papers  (2025-09-29T19:50:19Z)
• Accelerating Large-Scale Regularized High-Order Tensor Recovery [14.523033614261628]
  Existing tensor recovery methods fail to recognize the impact of scale variations on structural characteristics.<n>Existing studies face prohibitive computational costs dealing with large-scale high-order tensor data.
  arXiv  Detail & Related papers  (2025-06-11T10:53:07Z)
• A Bias-Correction Decentralized Stochastic Gradient Algorithm with Momentum Acceleration [19.83835152405735]
  We propose a momentum-celerated distributed gradient, termed Exact-Diffusion with Momentum (EDM)<n>EDM mitigates the bias from data heterogeneity and incorporates momentum techniques commonly used in deep learning.<n>Our theoretical analysis demonstrates that the EDM algorithm converges sublinearly to the neighborhood optimal solution.
  arXiv  Detail & Related papers  (2025-01-31T12:15:58Z)
• Conditional Mean and Variance Estimation via \ extit{k}-NN Algorithm with Automated Variance Selection [9.943131787772323]
  We introduce a novel textitk-nearest neighbor (textitk-NN) regression method for joint estimation of the conditional mean and variance.<n>The proposed algorithm preserves the computational efficiency and manifold-learning capabilities of classical non-parametric textitk-NN models.
  arXiv  Detail & Related papers  (2024-02-02T18:54:18Z)
• Online Variational Sequential Monte Carlo [49.97673761305336]
  We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference. Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
  arXiv  Detail & Related papers  (2023-12-19T21:45:38Z)
• Fast Learnings of Coupled Nonnegative Tensor Decomposition Using Optimal Gradient and Low-rank Approximation [7.265645216663691]
  We introduce a novel coupled nonnegative CANDECOMP/PARAFAC decomposition algorithm optimized by the alternating gradient method (CoNCPD-APG) By integrating low-rank approximation with the proposed CoNCPD-APG method, the proposed algorithm can significantly decrease the computational burden without compromising decomposition quality.
  arXiv  Detail & Related papers  (2023-02-10T08:49:36Z)
• An Accelerated Doubly Stochastic Gradient Method with Faster Explicit Model Identification [97.28167655721766]
  We propose a novel doubly accelerated gradient descent (ADSGD) method for sparsity regularized loss minimization problems. We first prove that ADSGD can achieve a linear convergence rate and lower overall computational complexity.
  arXiv  Detail & Related papers  (2022-08-11T22:27:22Z)
• Learning Distributionally Robust Models at Scale via Composite Optimization [45.47760229170775]
  We show how different variants of DRO are simply instances of a finite-sum composite optimization for which we provide scalable methods. We also provide empirical results that demonstrate the effectiveness of our proposed algorithm with respect to the prior art in order to learn robust models from very large datasets.
  arXiv  Detail & Related papers  (2022-03-17T20:47:42Z)
• Efficient Multidimensional Functional Data Analysis Using Marginal Product Basis Systems [2.4554686192257424]
  We propose a framework for learning continuous representations from a sample of multidimensional functional data. We show that the resulting estimation problem can be solved efficiently by the tensor decomposition. We conclude with a real data application in neuroimaging.
  arXiv  Detail & Related papers  (2021-07-30T16:02:15Z)
• Dual Optimization for Kolmogorov Model Learning Using Enhanced Gradient Descent [8.714458129632158]
  Kolmogorov model (KM) is an interpretable and predictable representation approach to learning the underlying probabilistic structure of a set of random variables. We propose a computationally scalable KM learning algorithm, based on the regularized dual optimization combined with enhanced gradient descent (GD) method. It is shown that the accuracy of logical relation mining for interpretability by using the proposed KM learning algorithm exceeds $80%$.
  arXiv  Detail & Related papers  (2021-07-11T10:33:02Z)
• Fractal Structure and Generalization Properties of Stochastic Optimization Algorithms [71.62575565990502]
  We prove that the generalization error of an optimization algorithm can be bounded on the complexity' of the fractal structure that underlies its generalization measure. We further specialize our results to specific problems (e.g., linear/logistic regression, one hidden/layered neural networks) and algorithms.
  arXiv  Detail & Related papers  (2021-06-09T08:05:36Z)
• Jointly Modeling and Clustering Tensors in High Dimensions [6.072664839782975]
  We consider the problem of jointly benchmarking and clustering of tensors. We propose an efficient high-maximization algorithm that converges geometrically to a neighborhood that is within statistical precision.
  arXiv  Detail & Related papers  (2021-04-15T21:06:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.