Garcke, Harald, Lam, Kei Fong and Styles, Vanessa (2018) Cahn--Hilliard inpainting with the double obstacle potential. SIAM Review, 11 (3). pp. 2064-2089. ISSN 0036-1445
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Abstract
The 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.
Item Type: | Article |
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Keywords: | inpainting, Cahn{Hilliard model, double obstacle potential, binary and grayvalue images |
Schools and Departments: | School of Mathematical and Physical Sciences > Mathematics |
Research Centres and Groups: | Numerical Analysis and Scientific Computing Research Group |
Subjects: | Q Science > QA Mathematics |
Depositing User: | Jodie Bacon |
Date Deposited: | 12 Oct 2018 11:31 |
Last Modified: | 12 Oct 2018 11:32 |
URI: | http://srodev.sussex.ac.uk/id/eprint/79377 |
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