<abstract xmlns="http://www.w3.org/1999/xhtml"><p> A novel anisotropic diffusion-based image denoising and restoration approach is proposed in this paper. A variational model for image restoration is introduced first, then the corresponding Euler-Lagrange equation being determined. A nonlinear parabolic PDE model is then obtained from this equation. It is based on a novel edge-stopping function and conductance parameter. A serious mathematical treatment is performed on this second-order anisotropic diffusion scheme, its well-possedness being investigated. Then, a consistent explicit numerical approximation scheme based on the finite difference method is developed for the proposed PDE model.</p></abstract>

A novel anisotropic diffusion-based image denoising and restoration approach is proposed in this paper. A variational model for image restoration is introduced first, then the corresponding Euler-Lagrange equation being determined. A nonlinear parabolic PDE model is then obtained from this equation. It is based on a novel edge-stopping function and conductance parameter. A serious mathematical treatment is performed on this second-order anisotropic diffusion scheme, its well-possedness being investigated. Then, a consistent explicit numerical approximation scheme based on the finite difference method is developed for the proposed PDE model.

Image Restoration using a Nonlinear Second-order Parabolic PDE-based Scheme

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Image Restoration using a Nonlinear Second-order Parabolic PDE-based Scheme"}

A novel anisotropic diffusion-based image denoising and restoration approach is proposed in this paper. A variational model for image restoration is introduced...

Image Restoration using a Nonlinear Second-order Parabolic PDE-based Scheme

Publié en ligne: 21 sept. 2017

Pages: 33 - 48

Reçu: 01 févr. 2016

Accepté: 01 avr. 2016

DOI: https://doi.org/10.1515/auom-2017-0003

Mots clés
image denoising and restoration, qualitative properties of solutions, boundary value problems for nonlinear parabolic PDE, Leray-Schauder principle, edge-stopping function, finite differences, numerical approximation scheme.

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Image Restoration using a Nonlinear Second-order Parabolic PDE-based Scheme

Publié en ligne: 21 sept. 2017

Pages: 33 - 48

Reçu: 01 févr. 2016

Accepté: 01 avr. 2016

DOI: https://doi.org/10.1515/auom-2017-0003

Mots clésimage denoising and restoration, qualitative properties of solutions, boundary value problems for nonlinear parabolic PDE, Leray-Schauder principle, edge-stopping function, finite differences, numerical approximation scheme.

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
image denoising and restoration, qualitative properties of solutions, boundary value problems for nonlinear parabolic PDE, Leray-Schauder principle, edge-stopping function, finite differences, numerical approximation scheme.