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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Badreddine Rjaibi,
  • Didier Auroux

摘要

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.