Fast Solvers for Cahn-Hilliard Inpainting

The solution of Cahn--Hilliard variational inequalities is of interest in many applications. We discuss the use of them as a tool for binary image inpainting. This has been done before using double-well potentials but not for nonsmooth potentials as considered here. The existing bound constraints are incorporated via the Moreau--Yosida regularization technique. We develop effective preconditioners for the efficient solution of the Newton steps associated with the fast solution of the Moreau--Yosida regularized problem. Numerical results illustrate the efficiency of our approach. Moreover, precise eigenvalue intervals are given for the preconditioned system using a double-well potential. A comparison between the smooth and nonsmooth Cahn--Hilliard inpainting models shows that the latter achieves better results.

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