用张量分解统一建模全局低秩与局部平滑，提升多维数据补全精度
LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion
- 基于Tucker分解融合低秩与平滑先验，自适应加权核范数+稀疏核心
- 在高缺失率下图像修复和交通数据补全任务中优于基线方法
- 无需调参的拉普拉斯正则化，适合对鲁棒性要求高的科学计算场景
多维数据补全是计算科学中的关键问题，广泛应用于计算机视觉、信号处理和科学计算。现有方法通常依赖全局低秩近似或局部平滑正则化，但各有局限：低秩方法计算昂贵且破坏数据内在结构，平滑方法需大量手动调参且泛化能力差。本文提出一种新的低秩Tucker表示模型（LRTuckerRep），在Tucker分解框架内统一建模全局与局部先验。具体而言，通过因子矩阵上的自适应加权核范数和稀疏的Tucker核心编码低秩性，利用因子空间上无参数的拉普拉斯正则化捕捉平滑性。为高效求解非凸优化问题，设计了两种具有收敛性保证的迭代算法。在多维图像修复与交通数据补全任务上的大量实验表明，该模型在高缺失率下仍能实现更优的补全精度与鲁棒性。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。