Wenwu Gong

Wenwu Gong, Lili Yang

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.

Yunshan Li, Wenwu Gong, Qianqian Wang et al.

Recent approaches based on transform-based tensor nuclear norm (TNN) have demonstrated notable effectiveness in hyperspectral image (HSI) inpainting by leveraging low-rank structures in latent representations. Recent developments incorporate deep transforms to improve low-rank tensor representation; however, existing approaches typically restrict the transform to the spectral mode, neglecting low-rank properties along other tensor modes. In this paper, we propose a novel 3-directional deep low-rank tensor representation (3DeepRep) model, which performs deep nonlinear transforms along all three modes of the HSI tensor. To enforce low-rankness, the model minimizes the nuclear norms of mode-i frontal slices in the corresponding latent space for each direction (i=1,2,3), forming a 3-directional TNN regularization. The outputs from the three directional branches are subsequently fused via a learnable aggregation module to produce the final result. An efficient gradient-based optimization algorithm is developed to solve the model in a self-supervised manner. Extensive experiments on real-world HSI datasets demonstrate that the proposed method achieves superior inpainting performance compared to existing state-of-the-art techniques, both qualitatively and quantitatively.

Wenwu Gong, Zhejun Huang, Lili Yang

In intelligent transportation systems, traffic data imputation, estimating the missing value from partially observed data is an inevitable and challenging task. Previous studies have not fully considered traffic data's multidimensionality and spatiotemporal correlations, but they are vital to traffic data recovery, especially for high-level missing scenarios. To address this problem, we propose a novel spatiotemporal regularized Tucker decomposition method. First, the traffic matrix is converted into a third-order tensor. Then, based on Tucker decomposition, the tensor is approximated by multiplying non-negative factor matrices with a sparse core tensor. Notably, we do not need to set the tensor rank or determine it through matrix nuclear-norm minimization or tensor rank minimization. The low rankness is characterized by the $l_1$-norm of the core tensor, while the manifold regularization and temporal constraint are employed to capture spatiotemporal correlations and further improve imputation performance. We use an alternating proximal gradient method with guaranteed convergence to address the proposed model. Numerical experiments show that our proposal outperforms matrix-based and tensor-based baselines on real-world spatiotemporal traffic datasets in various missing scenarios.