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

--Multi-dimensional data completion is a critical problem in computational sciences, particularly in domains such as computer vision and signal processing. 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 T ucker Representation (LRT uckerRep) model that unifies global and local prior modeling within a T ucker decomposition. T o 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 LRT uckerRep achieves superior completion accuracy and robustness under high missing rates compared to baselines. N the era of big data and artificial intelligence, multidimensional data with complex structures is increasingly prevalent across diverse domains, including computer vision, signal processing, and scientific computing. Tensor representations depict complex structural information from multidimensional data, which plays an important role in image science [1] and signal processing [2]. However, multidimensional data collected in practical applications suffers from degradation and information loss, affecting image enhancement quality and traffic prediction accuracy.