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ADMM algorithm for some regularized Perona–Malik equation and applications to image denoising

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Abstract

In this paper, we propose a new approach for solving the proposed variational model derived from Perona–Malik (PM) equation. This problem is the combination of P–M model and p-Laplacian operator. Our approach exploiting the different values of p (p near 1 or \(\infty \)) and using a variable contrast parameter \(\lambda \) to adaptively control the scattering pattern in the restored image. Firstly, we present the variational model, and we prove the existence and uniqueness of the minimizer. To solve numerically our problem, we apply the ADMM method to derive a robust scheme. Finally, we illustrate the effectiveness of our algorithm with various numerical tests which can compare favorably with some existing methods in the literature.

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Authors and Affiliations

  1. Ecole Supérieure de Technologie d’Essaouira, B.P. 383, Essaouira El Jadida, Essaouira, Morocco

    Farah Sniba, Fahd Karami & Driss Meskine

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  1. Farah Sniba
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  2. Fahd Karami
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  3. Driss Meskine
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Correspondence to Driss Meskine.

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Sniba, F., Karami, F. & Meskine, D. ADMM algorithm for some regularized Perona–Malik equation and applications to image denoising. SIViP 17, 609–617 (2023). https://doi.org/10.1007/s11760-022-02267-3

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  • DOI: https://doi.org/10.1007/s11760-022-02267-3

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