A nonconvex model combined with nonlocal self-similarity and tensor dictionary learning for robust tensor completion is proposed and outperforms the competing state-of-the-art methods in both visual quality and quantitative metrics.
Abstract
Robust tensor completion aims to recover a clean tensor from noisy and incomplete observations, where the observed tensor is corrupted by Gaussian noise and sparse noise simultaneously. Existing methods only exploit one or two priors out of global tensor low-rankness, local properties, and nonlocal self-similarity, leading to suboptimal recovery performance. In this paper, we propose a nonconvex model combined with nonlocal self-similarity and tensor dictionary learning for robust tensor completion. Specifically, by partitioning the tensor into several overlapping cubes, the similar cubes are grouped together. Then, we unfold the cubes into matrices and stack these matrices into a third-order tensor. Subsequently, the minimax concave penalty (MCP) is employed on the singular values of all frontal slices of the sub-tensors in the transformed domain to explore the low-rankness of the underlying sub-tensor. The tensor dictionary learning based on Tucker decomposition is used to explore the local patterns of the underlying sub-tensor. Moreover, the MCP is employed onto each entry of the sparse noise tensor to explore the sparsity. A proximal alternating linearized minimization algorithm is adopted to solve the resulting model. Extensive numerical experiments demonstrate that the proposed method outperforms the competing state-of-the-art methods in both visual quality and quantitative metrics.
A robust tensor recovery model based on second-order difference-induced adaptive tensor nuclear norm regularization that consistently improves PSNR and ERGAS under all tested noise settings while achieving competitive SSIM values is proposed.
Recently, tensor decompositions are prevalent for multi-dimensional image representation, which learn the instance-specific structure of each image from scratch. However, tensor decompositions neglect the common structure across different images, leading to limited semantic modeling capability, high computational cost, and a large number of learnable parameters. To address this challenge, we suggest the first pre-trained low-rank tensor decomposition (PLTD) framework, which organically integrates the pre-trained large vision model into the classical tensor decomposition framework. Beyond the shallow and untrained deep tensor decomposition, the suggested PLTD achieves an unprecedented balance among higher recovery fidelity, fewer learnable parameters, and smaller carbon footprint. Specifically, PLTD factorizes the target tensor into a latent tensor and a learnable transform that maps the latent tensor back to the original data domain. The latent tensor consists of two indispensable and complementary terms, i.e., a fixed pre-trained latent tensor and a learnable low-rank latent tensor. The fixed pre-trained latent tensor is distilled from a pre-trained large vision model (i.e., DINOv3) to capture the common structure of the target tensor, while the learnable low-rank latent tensor characterizes the instance-specific structure of the target tensor. To examine the potential of PLTD, we develop the corresponding multi-dimensional image recovery model and theoretically justify the advantages of this framework. Additionally, we discuss the connections between PLTD and classical tensor decomposition frameworks. Extensive experiments on multi-dimensional image recovery demonstrate that PLTD consistently achieves superior performance compared with state-of-the-art methods.
Bingfei Fu, Zhi-Long Han, Ting-Zhu Huang et al.· 0 citations
This paper proposes a novel Tensor Train (TT)-based tensor-on-tensor regression optimization framework for variable selection based on mode-1 hyperslice sparsity, and designs an alternating iterative algorithm equipped with a preconditioned metric to efficiently solve the proposed model.
This work provides a theoretical analysis which establishes a non-asymptotic reconstruction error bound that characterizes the effects of sampling complexity, optimization convergence, and model mismatch in a structured tensor approximation problem.
Jeongmin Chae, Usama Saleem, Selin Bac et al.· 0 citations
Low-rank tensor factorization provides a flexible framework for completing multidimensional data from incomplete and corrupted observations. However, unweighted spectral regularizers impose a common shrinkage profile across singular components, which may excessively attenuate dominant low-rank components, and factorized variants either lack component-specific weighting or require costly singular value decompositions (SVDs). This paper proposes two weighted Schatten-$p$ tensor factorization models, termed \WSpTFI{} and \WSpTFII{}, under the tensor-tensor product (t-product) framework to address these limitations. \WSpTFI{} is motivated by a factorized weighted tensor Schatten-$p$ norm identity and permits flexible, possibly asymmetric factor exponents. \WSpTFII{} constructs a regularizer from transform-domain column-pair energies, yielding SVD-free main factor updates and a column-pruning mechanism for reducing redundant rank components. This paper further develops an iteratively reweighted alternating direction method of multipliers (ADMM)-type scheme for \WSpTFI{} and an iteratively reweighted least squares (IRLS)--block successive upper-bound minimization (BSUM) scheme for \WSpTFII{}. Theoretical analysis establishes the weighted factorization relation and provides a conditional limiting Karush--Kuhn--Tucker (KKT) characterization for \WSpTFI{}. For \WSpTFII{}, the actual damped quadratic block updates yield a quantitative sufficient-decrease mechanism for the fixed-$\delta$ smoothed factor objective. This implies asymptotic regularity, and every accumulation point of the fixed-dimensional tail is stationary. Experiments on synthetic tensor completion, color-image restoration, hyperspectral inpainting, and printed-circuit-board defect detection demonstrate competitive reconstruction quality and robustness under various degradation conditions.
Bing-Hao Wang, Feng Zhang, Wen-Dong Wang et al.· 0 citations
Hyperspectral image (HSI) denoising remains a critical challenge due to noise corruption during acquisition. While nonlocal low-rank (LR) tensor methods leverage spatial–spectral correlations, they usually fail under heavy or complex noise, as directly estimating LR tensors from noisy observations usually leads to residual noise accumulation. To address this limitation, we propose a novel nonlocal low-rank residual (NLRR) approach, which reformulates LR tensor recovery as a progressive residual minimization problem. Unlike conventional methods that exclusively approximate LR tensors directly from degraded observations, the proposed NLRR approach iteratively refines the latent LR tensor structure by minimizing the rank residual, thereby decoupling noise suppression from tensor approximation. This residual-driven framework uniquely integrates two complementary priors: (1) a nonlocal LR residual prior that exploits spatial self-similarity, and (2) a global spectral LR prior that suppresses spectral redundancy. To generalize the proposed NLRR approach to real-world scenarios with mixed noise, we develop the NLRR-robust principal component analysis (NLRR-RPCA) framework, which incorporates the LR residual along with global spectral LR and sparse tensor priors for mixed noise removal. Additionally, to ensure both numerical stability and computational tractability, we develop an adaptive rank-adjusted alternating minimization algorithm, which dynamically adjusts the ranks of the estimated tensors to better handle different noise scenarios. Extensive experiments on both simulated and real HSI datasets demonstrate that our proposed NLRR approach outperforms numerous popular or state-of-the-art methods in both quantitative evaluation and visual perception.
Lixia Xia, Youqun Chen, Xin Wang et al.· Mathematics· 0 citations
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