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Deep image prior and weighted anisotropic-isotropic total variation regularization for solving linear inverse problems

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  • Xie, Yujia
  • Chen, Wengu
  • Ge, Huanmin
  • Ng, Michael K.

Abstract

Deep learning, particularly unsupervised techniques, has been widely used to solve linear inverse problems due to its flexibility. A notable unsupervised approach is the deep image prior (DIP), which employs a predetermined deep neural network to regularize inverse problems by imposing constraints on the generated image. This article introduces an optimization technique (DIP-AITV) by combining the DIP with the weighted anisotropic-isotropic total variation (AITV) regularization. Furthermore, we utilize the alternating direction method of multipliers (ADMM), a highly flexible optimization technique, to solve the DIP-AITV minimization problem effectively. To demonstrate the benefits of the proposed DIP-AITV method over the state-of-the-art DIP, DIP-TV, DIP-WTV and CS-DIP, we solve two linear inverse problems, i.e., image denoising and compressed sensing. Computation examples on the MSE and PSNR values show that our method outperforms the existing DIP-based methods in both synthetic and real grayscale and color images.

Suggested Citation

  • Xie, Yujia & Chen, Wengu & Ge, Huanmin & Ng, Michael K., 2024. "Deep image prior and weighted anisotropic-isotropic total variation regularization for solving linear inverse problems," Applied Mathematics and Computation, Elsevier, vol. 482(C).
    • Handle: RePEc:eee:apmaco:v:482:y:2024:i:c:s0096300324004132
    DOI: 10.1016/j.amc.2024.128952
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    References listed on IDEAS

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    1. Wang, Chengxiang & Wang, Xiaoyan & Zhao, Kequan & Huang, Min & Li, Xianyun & Yu, Wei, 2023. "A cascading l0 regularization reconstruction method in nonsubsampled contourlet domain for limited-angle CT," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    2. Cascarano, Pasquale & Piccolomini, Elena Loli & Morotti, Elena & Sebastiani, Andrea, 2022. "Plug-and-Play gradient-based denoisers applied to CT image enhancement," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    3. Liu, Jingjing & Ma, Ruijie & Zeng, Xiaoyang & Liu, Wanquan & Wang, Mingyu & Chen, Hui, 2021. "An efficient non-convex total variation approach for image deblurring and denoising," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    4. Wang, Yugang & Huang, Ting-Zhu & Zhao, Xi-Le & Deng, Liang-Jian & Ji, Teng-Yu, 2020. "A convex single image dehazing model via sparse dark channel prior," Applied Mathematics and Computation, Elsevier, vol. 375(C).
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