__its-home.uscs.susx.ac.uk_home_jb622_Documents_Receptionist Files_Research Papers_Cahn-Hilliard Inpainting with the Double Obstacle Potential.pdf (2.48 MB)
Cahn--Hilliard inpainting with the double obstacle potential
journal contribution
posted on 2023-06-09, 15:27 authored by Harald Garcke, Kei Fong Lam, Vanessa StylesVanessa StylesThe inpainting of damaged images has a wide range of applications, and many different mathematical methods have been proposed to solve this problem. Inpainting with the help of Cahn{Hilliard models has been particularly successful, and it turns out that Cahn{Hilliard inpainting with the double obstacle potential can lead to better results compared to inpainting with a smooth double well potential. However, a mathematical analysis of this approach is missing so far. In this paper we give first analytical results for a Cahn--Hilliard double obstacle inpainting model regarding existence of global solutions to the time-dependent problem and stationary solutions to the time-independent problem without constraints on the parameters involved. With the help of numerical results we show the effectiveness of the approach for binary and grayscale images.
Funding
Regensburger Universit?atsstiftung Hans Vielberth
History
Publication status
- Published
File Version
- Published version
Journal
SIAM Journal on Imaging SciencesISSN
1936-4954Publisher
Society for Industrial and Applied MathematicsExternal DOI
Issue
3Volume
11Page range
2064-2089Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Numerical Analysis and Scientific Computing Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes