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Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 2/2023

03.10.2022 | Original Research

A denoising model based on the fractional Beltrami regularization and its numerical solution

verfasst von: Anouar Ben-Loghfyry, Abdelilah Hakim, Amine Laghrib

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 2/2023

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Abstract

In image processing, the regularization term is always hard to choose. In this paper, we introduce a model based on the fractional derivative, which is derived from the classical Beltrami model. The proposed regularization term offers an ideal compromise between feature preservation, avoidance of staircasing and the loss of image contrasts. This model can outperform the high order regularization models and also the total fractional-order variation model. Also, we rigorously analyse the theoretical properties of the fractional derivative and show the existence and uniqueness of the proposed minimization problem in a suitable functional framework. In addition, to solve the variational problem, we consider the primal-dual projected gradient algorithm. Numerical experiments show that the proposed model produces competitive results compared to some classical regularizations, especially, it avoids the staircase effect and preserves edges and features of the image while reducing noise.
Vorheriger Artikel Convergence rate analysis of an extrapolated proximal difference-of-convex algorithm
Nächster Artikel New iterative methods for finding solutions of Hammerstein equations

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Metadaten
Titel
A denoising model based on the fractional Beltrami regularization and its numerical solution
verfasst von
Anouar Ben-Loghfyry
Abdelilah Hakim
Amine Laghrib
Publikationsdatum
03.10.2022
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 2/2023
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-022-01798-9

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