Low-Rank Regularized Joint Sparsity Modeling for Image Denoising

ZHA Zhiyuan; YUAN Xin; ZHANG Jiachao; ZHU Ce

doi:10.11999/JEIT240324

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ZHA Zhiyuan, YUAN Xin, ZHANG Jiachao, ZHU Ce. Low-Rank Regularized Joint Sparsity Modeling for Image Denoising[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT240324

Citation:

ZHA Zhiyuan, YUAN Xin, ZHANG Jiachao, ZHU Ce. Low-Rank Regularized Joint Sparsity Modeling for Image Denoising[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT240324

ZHA Zhiyuan, YUAN Xin, ZHANG Jiachao, ZHU Ce. Low-Rank Regularized Joint Sparsity Modeling for Image Denoising[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT240324

Citation:

ZHA Zhiyuan, YUAN Xin, ZHANG Jiachao, ZHU Ce. Low-Rank Regularized Joint Sparsity Modeling for Image Denoising[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT240324

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Low-Rank Regularized Joint Sparsity Modeling for Image Denoising

doi: 10.11999/JEIT240324

1.
College of Communication Engineering, Jilin University, Changchun 130012, China
2.
School of Engineering, Westlake University, Hangzhou 310024, China
3.
Artificial Intelligence Institute of Industrial Technology, Nanjing Institute of Technology, Nanjing 211167, China
4.
School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

Funds: The National Natural Science Foundation of China (62471199, 62020106011, 62271414, 61971476, 62002160 and 62072238), Start-up Grant from the Tang Aoqing talent professor of Jilin University, Science Fund for Distinguished Young Scholars of Zhejiang Province (LR23F010001), and Westlake Foundation (2023GD007)

Received Date: 2024-04-23
Rev Recd Date: 2025-01-24

Available Online: 2025-02-09

Abstract

Abstract

Objective Image denoising aims to reduce unwanted noise in images, which has been a long-standing issue in imaging science. Noise significantly degrades image quality, affecting their use in applications such as medical imaging, remote sensing, and image reconstruction. Over recent decades, various image prior models have been developed to address this problem, focusing on different image characteristics. These models, utilizing priors like sparsity, Low-Rankness (LR), and Nonlocal Self-Similarity (NSS), have proven highly effective. Nonlocal sparse representation models, including Joint Sparsity (JS), LR, and Group Sparse Representation (GSR), effectively leverage the NSS property of images. They capture the structural similarity of image patches, even when spatially distant. Popular dictionary-based JS algorithms use a relaxed convex penalty to avoid NP-hard sparse coding, leading to an approximately sparse representation. However, these approximations fail to enforce LR on the image data, reducing denoising quality, especially in cases of complex noise patterns or high self-similarity. This paper proposes a novel Low-Rank Regularized Joint Sparsity (LRJS) model for image denoising, integrating the benefits of LR and JS priors. The LRJS model enhances denoising performance, particularly where traditional methods underperform. By exploiting the NSS in images, the LRJS model better preserves fine details and structures, offering a robust solution for real-world applications. Methods The proposed LRJS model integrates low-rank and JS priors to enhance image denoising performance. By exploiting the NSS property of images, the LRJS model strengthens the dependency between nonlocal similar patches, improving image structure representation and noise suppression. The low-rank prior reflects the smoothness and regularity inherent in the image, whereas the JS prior captures the sparsity of the image patches. Incorporating these priors ensures a more accurate representation of the underlying clean image, enhancing denoising performance. An alternating minimization algorithm is proposed to solve this optimization problem, alternating between the low-rank and JS terms to simplify the optimization process. Additionally, an adaptive parameter adjustment strategy dynamically tunes the regularization parameters, balancing LR and sparsity throughout the optimization. The LRJS model offers an effective approach for image denoising by combining low-rank and JS priors, solved using an alternating minimization framework with adaptive parameter tuning. Results and Discussions Experimental results on two image denoising tasks, Gaussian noise removal (Fig. 4, Fig. 5, Table 3, Table 4) and Poisson denoising (Fig. 6, Table 5), demonstrate that the proposed LRJS method outperforms several popular and state-of-the-art denoising algorithms in both objective metrics and visual perceptual quality, particularly for images with high self-similarity. In Gaussian noise removal, the LRJS method achieves significant improvements, especially with highly self-similar images. This improvement results from LRJS effectively leveraging the NSS prior, which strengthens the dependencies among similar patches, leading to better noise suppression while preserving image details. Compared with other methods, LRJS demonstrates greater robustness, particularly in retaining fine details and structures often lost with traditional denoising techniques. For Poisson denoising, the LRJS method also yields notable performance gains. It better manages the complexity of Poisson noise compared with other approaches, highlighting its versatility and robustness across different noise types. The visual quality of the denoised images shows fewer artifacts and more accurate recovery of details. Quantitative results in terms of PSNR and SSIM further validate the effectiveness of LRJS, positioning it as a competitive solution in image denoising. Overall, these experimental findings confirm that LRJS offers a reliable and effective approach, particularly for images with high self-similarity and complex noise models. Conclusions The LRJS model proposed in this paper improves image denoising performance by combining LR and JS priors. This dual-prior framework better captures the underlying image structure while suppressing noise, particularly benefiting images with high self-similarity. Experimental results demonstrate that the LRJS method not only outperforms traditional denoising techniques but also exceeds many state-of-the-art algorithms in both objective metrics and visual quality. By leveraging the NSS property of image patches, the LRJS model enhances the dependencies among similar patches, making it particularly effective for tasks requiring the preservation of fine details and structures. The LRJS method significantly enhances the quality of denoised images, especially in complex noise scenarios such as Gaussian and Poisson noise. Its robust alternating minimization algorithm with adaptive parameter adjustment ensures effective optimization, contributing to superior performance. The results further highlight the LRJS model’s ability to preserve image edges, textures, and other fine details often degraded in other denoising algorithms. Compared with existing techniques, the LRJS method demonstrates superior performance in handling high noise levels while maintaining image clarity and detail, making it a promising tool for applications such as medical imaging, remote sensing, and image restoration. Future research could focus on optimizing the model for more complex noise environments, such as mixed noise or real-world noise that is challenging to model. Additionally, exploring more efficient algorithms and integrating advanced techniques, such as deep learning, may further improve the LRJS model’s capability and applicability to diverse denoising tasks.
- Image denoising,
- Poisson denoising,
- Nonlocal sparse representation,
- Low-Rank Regularized Joint Sparsity (LRJS),
- Alternating minimization,
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References(36)

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