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Cahn--Hilliard inpainting with the double obstacle potential

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posted on 2023-06-09, 15:27 authored by Harald Garcke, Kei Fong Lam, Vanessa StylesVanessa Styles
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.

Funding

Regensburger Universit?atsstiftung Hans Vielberth

History

Publication status

  • Published

File Version

  • Published version

Journal

SIAM Journal on Imaging Sciences

ISSN

1936-4954

Publisher

Society for Industrial and Applied Mathematics

Issue

3

Volume

11

Page range

2064-2089

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Numerical Analysis and Scientific Computing Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-10-12

First Open Access (FOA) Date

2018-10-12

First Compliant Deposit (FCD) Date

2018-10-11

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