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An improved nonlinear anisotropic PDE with p(x)-growth conditions applied to image restoration and enhancement
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  • Hamza Alaa,
  • Nour Eddine Alaa,
  • Anass Bouchriti,
  • Abderrahim CHARKAOUI
Hamza Alaa
Cadi Ayyad University Faculty of Science and Technology Gueliz

Corresponding Author:[email protected]

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Nour Eddine Alaa
Cadi Ayyad University Faculty of Science and Technology Gueliz
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Anass Bouchriti
Cadi Ayyad University Faculty of Science and Technology Gueliz
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Abderrahim CHARKAOUI
Cadi Ayyad University Faculty of Science and Technology Gueliz
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Abstract

This work proposes a novel nonlinear parabolic equation with p(x)-growth conditions for image restoration and enhancement. Based on the generalized Lebesgue and Sobolev spaces with variable exponent, we demonstrate the well-posedness of the proposed model. As a first result, we prove the existence of a weak solution to our model when the reaction term is bounded by a suitable function. Secondly, we use the approximations method to establish the existence of a nonnegative weak SOLA solution (Solution Obtained as Limit of Approximations) to the proposed model. Finally, numerical experiments illustrate that the proposed model performs better for image enhancement and denoising.
06 Jul 2022Submitted to Mathematical Methods in the Applied Sciences
07 Jul 2022Submission Checks Completed
07 Jul 2022Assigned to Editor
28 Jul 2022Reviewer(s) Assigned
04 Feb 2024Review(s) Completed, Editorial Evaluation Pending
05 Feb 2024Editorial Decision: Accept