Speckle noise removal in color images using a generalized nonstandard fourth-order variational method

Badreddine Rjaibi () and Didier Auroux ()
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Badreddine Rjaibi: Université de Tunis El Manar, Ecole Nationale d’Ingénieurs de Tunis
Didier Auroux: Université Côte d’Azur

Partial Differential Equations and Applications, 2025, vol. 6, issue 4, 1-30

Abstract: Abstract In this work, we propose a generalized nonstandard fourth-order variational model to remove speckle noise in color images. This method is based on finding the minimum of the q(.) and p(.)-Kirchhoff energy in a specified Banach space. First, we study the existence and uniqueness of the solution for the q(.)-biharmonic and p(.)-Laplacian Euler equations associated with the proposed energy. Then, we consider a fully-discrete forward Euler–Galerkin semi-implicit scheme to find the numerical solution and we study its convergence towards the continuous solution. In the resolution algorithm, the variable exponent functions p(.) and q(.) are chosen adaptively, based on the Di Zenzo gradient and p(.)-Laplacian operator of the image in order to preserve edges and thin structures. Finally, we illustrate the efficiency of our approach with several numerical results.

Keywords: Speckle noise removal; Kirchhoff energy; Di Zenzo gradient; Biharmonic operator; 35Gxx; 49Mxx; 68U10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00340-3

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