Fast Solvers for Cahn--Hilliard Inpainting

Jessica Bosch, David Kay, Martin Stoll, Andrew J. Wathen

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


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. © 2014 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)67-97
Number of pages31
JournalSIAM Journal on Imaging Sciences
Issue number1
StatePublished - Jan 2 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


Dive into the research topics of 'Fast Solvers for Cahn--Hilliard Inpainting'. Together they form a unique fingerprint.

Cite this