Automated finite element solution of diffusion models for image denoising

DOI10.2478/tmmp-2023-0002OpenAlexW4323356264WikidataQ126092330 ScholiaQ126092330MaRDI QIDQ2689385

Abderrazzak Boufala, El Mostafa Kalmoun

Publication date: 10 March 2023

Published in: Tatra Mountains Mathematical Publications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/tmmp-2023-0002

zbMATH Keywords

total variationfinite element methodpartial differential equationsimage denoisingFEniCSPerona-Malik methoddiffusivity function

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08)

Uses Software

• FEniCS
• Python
• hIPPYlib
• DUNE-ACFem
• DefElement

Cites Work

• Nonlinear total variation based noise removal algorithms
• An adaptive finite element method in \(L^2\)-TV-based image denoising
• Automated solution of differential equations by the finite element method. The FEniCS book
• Relations between regularization and diffusion filtering
• Approximating the total variation with finite differences or finite elements
• Total Variation Minimization with Finite Elements: Convergence and Iterative Solution
• Solving PDEs in Python
• Introduction to Numerical Methods for Variational Problems
• hIPPYlib

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