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

TL;DR

This paper introduces a scalable, efficient tensor-based data recovery method that improves computational speed and modeling accuracy for multi-dimensional data using randomized algorithms and advanced optimization techniques.

Contribution

It proposes a novel FCTN-based nonconvex regularization framework with randomized compression algorithms for scalable multi-dimensional data recovery.

Findings

Outperforms state-of-the-art methods in accuracy and speed

Provides theoretical guarantees on convergence and approximation error

Demonstrates effectiveness through extensive numerical experiments

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.