KAUST Grant NumberKUK-C1-013-04
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AbstractThe 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. © 2014 Society for Industrial and Applied Mathematics.
CitationBosch J, Kay D, Stoll M, Wathen AJ (2014) Fast Solvers for Cahn--Hilliard Inpainting. SIAM Journal on Imaging Sciences 7: 67–97. Available: http://dx.doi.org/10.1137/130921842.
SponsorsThis research was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
JournalSIAM Journal on Imaging Sciences