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<p>In this paper, we study a second-order nonlinear problem involving non-local diffusion for image processing. The proposed model is derived by interpreting the dynamics of image processing as damped elastic deformation. This approach highlights the link between the second-order model and accelerated methods for the associated energy. Using Schauder’s fixed point theorem, we prove the well-posedness of the solution of the proposed model. The model is discretized and its solution calculated using the finite difference method. To illustrate the efficiency of our model, we perform denoising experiments and compare the results with existing models in the literature.</p>

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A nonlinear second order problem involving nonlocal diffusion for image processing

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Fatiha Bendaida,
  • Fahd Karami,
  • Driss Meskine,
  • Khadija Sadik,
  • Lamia Ziad

摘要

In this paper, we study a second-order nonlinear problem involving non-local diffusion for image processing. The proposed model is derived by interpreting the dynamics of image processing as damped elastic deformation. This approach highlights the link between the second-order model and accelerated methods for the associated energy. Using Schauder’s fixed point theorem, we prove the well-posedness of the solution of the proposed model. The model is discretized and its solution calculated using the finite difference method. To illustrate the efficiency of our model, we perform denoising experiments and compare the results with existing models in the literature.