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Image Restoration with Fractional-Order Total Variation Regularization and Group Sparsity

Author

Listed:
  • Jameel Ahmed Bhutto

    (School of Computer, Huanggang Normal University, Huanggang 438000, China)

  • Asad Khan

    (Metaverse Research Institute, School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China)

  • Ziaur Rahman

    (School of Computer, Huanggang Normal University, Huanggang 438000, China)

Abstract

In this paper, we present a novel image denoising algorithm, specifically designed to effectively restore both the edges and texture of images. This is achieved through the use of an innovative model known as the overlapping group sparse fractional-order total variation regularization model (OGS-FOTVR). The OGS-FOTVR model ingeniously combines the benefits of the fractional-order (FO) variation domain with an overlapping group sparsity measure, which acts as its regularization component. This is further enhanced by the inclusion of the well-established L2-norm, which serves as the fidelity term. To simplify the model, we employ the alternating direction method of multipliers (ADMM), which breaks down the model into a series of more manageable sub-problems. Each of these sub-problems can then be addressed individually. However, the sub-problem involving the overlapping group sparse FO regularization presents a high level of complexity. To address this, we construct an alternative function for this sub-problem, utilizing the mean inequality principle. Subsequently, we employ the majorize-minimization (MM) algorithm to solve it. Empirical results strongly support the effectiveness of the OGS-FOTVR model, demonstrating its ability to accurately recover texture and edge information in images. Notably, the model performs better than several advanced variational alternatives, as indicated by superior performance metrics across three image datasets, PSNR, and SSIM.

Suggested Citation

  • Jameel Ahmed Bhutto & Asad Khan & Ziaur Rahman, 2023. "Image Restoration with Fractional-Order Total Variation Regularization and Group Sparsity," Mathematics, MDPI, vol. 11(15), pages 1-23, July.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3302-:d:1203891
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    References listed on IDEAS

    as
    1. Ding, Meng & Huang, Ting-Zhu & Wang, Si & Mei, Jin-Jin & Zhao, Xi-Le, 2019. "Total variation with overlapping group sparsity for deblurring images under Cauchy noise," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 128-147.
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