Numerical Linear Algebra for the Two-Dimensional Bertozzi–Esedoglu–Gillette–Cahn–Hilliard Equation in Image Inpainting-Reference-Cited by-同舟云学术

Numerical Linear Algebra for the Two-Dimensional Bertozzi–Esedoglu–Gillette–Cahn–Hilliard Equation in Image Inpainting

Published:2023-12-14 Issue:24 Volume:11 Page:4952
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Awad Yahia¹^ORCID,Fakih Hussein¹²³^ORCID,Alkhezi Yousuf⁴^ORCID

Affiliation:

1. Department of Mathematics and Physics, Bekaa Campus, Lebanese International University (LIU), Al-Khyara P.O. Box 5, Lebanon

2. Department of Mathematics and Physics, Beirut Campus, The International University of Beirut (BIU), Beirut P.O. Box 1001, Lebanon

3. Khawarizmi Laboratory for Mathematics and Applications, Department of Mathematics, Lebanese University, Beirut P.O. Box 1001, Lebanon

4. Mathematics Department, College of Basic Education, Public Authority for Applied Education and Training (PAAET), P.O. Box 34053, Kuwait City 70654, Kuwait

Abstract

In this paper, we present a numerical linear algebra analytical study of some schemes for the Bertozzi–Esedoglu–Gillette–Cahn–Hilliard equation. Both 1D and 2D finite difference discretizations in space are proposed with semi-implicit and implicit discretizations on time. We prove that our proposed numerical solutions converge to continuous solutions.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/24/4952/pdf

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4. Kokaram, A.C. (1998). Motion Picture Restoration: Digital Algorithms for Artefact Suppression in Degraded Motion Picture Film and Video, Springer.

5. Akeley, K. (2000, January 23–28). Image inpainting. Proceedings of the 27th Internationl Conference on Computer Graphics and Interactive Techniques Conference SIGGRAPH 2000, New Orleans, LA, USA.

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