Hyperspectral Image Denoising Algorithm via Joint Low-Rank Tensor Decomposition and Product Graph Modeling

MA Mou; CAI Mingjiao; SHEN Yu; ZHOU Fang; JIANG Junzheng

doi:10.11999/JEIT250130

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MA Mou, CAI Mingjiao, SHEN Yu, ZHOU Fang, JIANG Junzheng. Hyperspectral Image Denoising Algorithm via Joint Low-Rank Tensor Decomposition and Product Graph Modeling[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250130

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MA Mou, CAI Mingjiao, SHEN Yu, ZHOU Fang, JIANG Junzheng. Hyperspectral Image Denoising Algorithm via Joint Low-Rank Tensor Decomposition and Product Graph Modeling[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250130

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Hyperspectral Image Denoising Algorithm via Joint Low-Rank Tensor Decomposition and Product Graph Modeling

doi: 10.11999/JEIT250130 cstr: 32379.14.JEIT250130

1.
School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China
2.
School of Information Engineering, China Jiliang University, Hangzhou 310018, China
3.
Hangzhou Institute of Technology, Xidian University, Hangzhou 311231, China

Funds: The National Natural Science Foundation of China (62171146, 62261014), Guangxi Natural Science Foundation for Distinguished Young Scholar (2021GXNSFFA220004), Hangzhou Joint Fund of the Zhejiang Provincial Natural Science Foundation of China (LHZSZ25F010003)

Received Date: 2025-03-05
Rev Recd Date: 2025-07-14

Available Online: 2025-07-24

Abstract

Abstract

Various types of noise in HyperSpectral Images (HSI) can severely degrade subsequent analysis. To address this problem, this study proposes a denoising framework based on Low-Rank Tensor Decomposition and Kronecker product Graph Laplacian Regularization (LRTDKGLR). Spatial and spectral graphs are constructed using Graph Signal Processing (GSP) and fused into a joint spatial-spectral product graph through the Kronecker product. Tucker decomposition is applied to this product graph to extract a unified low-dimensional representation, capturing the global spatial and spectral structures. A Kronecker Graph Laplacian Regularization (KGLR) term is introduced to enforce piecewise smoothness across both spatial and spectral dimensions, enhancing inter-band coherence. The denoising problem is formulated as an optimization task that integrates low-rank decomposition and graph-based regularization, solved efficiently using an Augmented Lagrangian Multiplier (ALM) approach. Experimental results on simulated and real HSI datasets demonstrate that LRTDKGLR achieves superior performance in edge preservation and noise suppression compared with existing HSI denoising methods. Objective Traditional denoising approaches often fail to simultaneously preserve spatial details and spectral fidelity due to the high dimensionality and complex spectral characteristics of HSI data. This study aims to develop a method that effectively suppresses mixed noise, such as Gaussian and stripe noise, while preserving critical spatial features and edge structures. The proposed approach leverages LRTDKGLR to enhance inter-dimensional correlations between spatial and spectral domains, ensuring improved noise reduction and detail preservation. Additionally, this research investigates an efficient ALM-based optimization strategy to address the HSI denoising problem, providing a more robust solution for noise reduction in high-dimensional, contaminated environments. Methods The proposed LRTDKGLR algorithm performs HSI denoising by effectively modeling spatial-spectral correlations. Separate spatial and spectral graphs are constructed and integrated through the Kronecker product to form a unified product graph representation. This joint graph considers both pixel intensity and the values of neighboring pixels across spatial and spectral dimensions, enabling enhanced denoising through spatial–spectral correlation modeling. Tucker decomposition is applied to extract a low-rank representation that captures global spatial-spectral relationships within the data. This decomposition facilitates effective modeling of the inherent structure of HSI while supporting the denoising process. The KGLR term models smoothness across both spatial and spectral domains, preserving essential spatial details and spectral continuity. The denoising task is formulated as an optimization problem that integrates low-rank tensor decomposition and KGLR. This problem is efficiently solved using the ALM method. The proposed approach achieves a balance between noise suppression and detail preservation, providing an effective solution for HSI denoising in high-dimensional, noisy conditions. Results and Discussions The proposed LRTDKGLR algorithm effectively exploits the inherent spatial and spectral correlations in HSI data. By incorporating a low-rank constraint and leveraging the similarity between adjacent spectral bands, the model enhances its capacity to capture inter-band spectral dependencies. Fig. 2 illustrates the denoising performance of various algorithms under Scenario 3, which combines Gaussian and impulse noise, applied to the 106th band of the Washington DC Mall dataset. A magnified view of a local region is also provided. The LRTV, LRTDTV, and LRTDGTV algorithms remove most of the noise but introduce over-smoothing, resulting in the loss of important edge structures. The NGmeet algorithm performs less effectively due to insufficient utilization of spatial neighborhood relationships. Although the LRMR, GLF, and TSLRLN algorithms reduce part of the noise, residual artifacts persist and over-smoothing remains evident. In contrast, the proposed LRTDKGLR algorithm demonstrates substantially improved denoising performance, supported by both visual comparisons and quantitative metrics. Fig. 3 presents the PSNR and SSIM values across multiple spectral bands under Scenario 3. The proposed method achieves higher performance in both metrics across most bands, indicating enhanced noise suppression and improved preservation of structural details. Numerical results summarized in Table 2 further confirm the effectiveness of the proposed approach, which consistently outperforms competing algorithms under identical conditions, providing superior denoising performance. Additionally, Table 3 shows that LRTDKGLR exceeds two representative deep learning-based methods, HSID-CNN and HSI-SDeCNN, across different noise levels. These findings demonstrate the robustness of the proposed method in the presence of Gaussian noise. Compared with deep learning-based approaches, LRTDKGLR offers practical advantages, including no requirement for pre-training, ease of deployment, and higher computational efficiency, which collectively improve its applicability to real-world HSI denoising tasks. Conclusions This study proposes an HSI denoising algorithm, LRTDKGLR, which integrates low-rank prior knowledge with a product graph model. The algorithm models HSI data as a product graph using GSP theory and applies Tucker decomposition to extract a core tensor and factor matrices, effectively capturing global spatial and spectral correlations. Simultaneously, KGLR is employed to model piecewise smoothness in both spatial and spectral dimensions, enhancing the representation of inter-dimensional relationships within the data. The denoising task is formulated as an optimization problem that combines low-rank tensor decomposition with KGLR constraints and is efficiently solved using the ALM method. Experimental results on simulated and real-world datasets demonstrate that the proposed LRTDKGLR algorithm achieves superior noise suppression while preserving structural details, validating its effectiveness for HSI denoising.
- Hyperspectral image denoising,
- Product graph model,
- Tucker decomposition,
- Augmented Lagrangian multiplier (ALM)

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References(22)

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