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Cahn-Hilliard inpainting with the double obstacle potential. (English) Zbl 1455.94019

Summary: 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.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
68U10 Computing methodologies for image processing
35K55 Nonlinear parabolic equations
49J40 Variational inequalities

Software:

ALBERTA
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Full Text: DOI arXiv

References:

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