  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.
