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Regularized Perona & Malik model involving Caputo time-fractional derivative with application to image denoising

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  • Ben-Loghfyry, Anouar
  • Charkaoui, Abderrahim

Abstract

This work tackles a novel partial differential equation based on a time-fractional order derivative for image denoising and restoration. We ameliorate the classical Perona–Malik model by considering Caputo time-fractional order derivative with a regularized diffusion. We start by investigating the existence of the solution to the proposed model. As a first result, we use the Faedo–Galerkin approach to prove the existence and uniqueness of a weak solution to an auxiliary fractional problem. Secondly, we establish the existence and uniqueness of a weak solution to our model via Schauder fixed point method. To validate the efficiency of our model, we present some numerical experiments on images with different features and various noise levels. We begin by introducing an adaptive discrete scheme to the proposed model. We illustrate the sensitivity of the time-fractional order derivative with respect to some well-known criteria. Finally, the obtained numerical results show a great efficiency and robustness against noise compared to the competitive models.

Suggested Citation

  • Ben-Loghfyry, Anouar & Charkaoui, Abderrahim, 2023. "Regularized Perona & Malik model involving Caputo time-fractional derivative with application to image denoising," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008263
    DOI: 10.1016/j.chaos.2023.113925
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    1. Pitsik, Elena N. & Maximenko, Vladimir A. & Kurkin, Semen A. & Sergeev, Alexander P. & Stoyanov, Drozdstoy & Paunova, Rositsa & Kandilarova, Sevdalina & Simeonova, Denitsa & Hramov, Alexander E., 2023. "The topology of fMRI-based networks defines the performance of a graph neural network for the classification of patients with major depressive disorder," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
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    Cited by:

    1. Zeng, Yue & Zhang, Yao-jia & Huang, Nan-jing, 2024. "A stochastic fractional differential variational inequality with Lévy jump and its application," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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