{"ID":2886735,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.03755","arxiv_id":"2508.03755","title":"LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion","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.","short_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 lim...","url_abs":"https://arxiv.org/abs/2508.03755","url_pdf":"https://arxiv.org/pdf/2508.03755v1","authors":"[\"Wenwu Gong\",\"Lili Yang\"]","published":"2025-08-04T06:57:50Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CV\",\"math.NA\"]","methods":"[]","has_code":false}