LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion

• URL: http://arxiv.org/abs/2508.03755v1
• Date: Mon, 04 Aug 2025 06:57:50 GMT
• Title: LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion
• Authors: Wenwu Gong, Lili Yang,
• Abstract summary: Multi-dimensional data completion is a critical problem in computational sciences.<n>We propose a novel Low-Rank Tucker Representation (LRTuckerRep) model that unifies global and local prior within a Tucker decomposition.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Multi-dimensional data completion is a critical problem in computational sciences, particularly in domains such as computer vision, signal processing, and scientific computing. Existing methods typically leverage either global low-rank approximations or local smoothness regularization, but each suffers from notable limitations: low-rank methods are computationally expensive and may disrupt intrinsic data structures, while smoothness-based approaches often require extensive manual parameter tuning and exhibit poor generalization. In this paper, we propose a novel Low-Rank Tucker Representation (LRTuckerRep) model that unifies global and local prior modeling within a Tucker decomposition. Specifically, LRTuckerRep encodes low rankness through a self-adaptive weighted nuclear norm on the factor matrices and a sparse Tucker core, while capturing smoothness via a parameter-free Laplacian-based regularization on the factor spaces. To efficiently solve the resulting nonconvex optimization problem, we develop two iterative algorithms with provable convergence guarantees. Extensive experiments on multi-dimensional image inpainting and traffic data imputation demonstrate that LRTuckerRep achieves superior completion accuracy and robustness under high missing rates compared to baselines.

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