Handle URI:
http://hdl.handle.net/10754/598319
Title:
Fast Solvers for Cahn--Hilliard Inpainting
Authors:
Bosch, Jessica; Kay, David; Stoll, Martin; Wathen, Andrew J.
Abstract:
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.
Citation:
Bosch 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.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Imaging Sciences
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
2-Jan-2014
DOI:
10.1137/130921842
Type:
Article
ISSN:
1936-4954
Sponsors:
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).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorBosch, Jessicaen
dc.contributor.authorKay, Daviden
dc.contributor.authorStoll, Martinen
dc.contributor.authorWathen, Andrew J.en
dc.date.accessioned2016-02-25T13:18:38Zen
dc.date.available2016-02-25T13:18:38Zen
dc.date.issued2014-01-02en
dc.identifier.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.en
dc.identifier.issn1936-4954en
dc.identifier.doi10.1137/130921842en
dc.identifier.urihttp://hdl.handle.net/10754/598319en
dc.description.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.en
dc.description.sponsorshipThis 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).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectBinary imagesen
dc.subjectCahn-Hilliard equationen
dc.subjectImage inpaintingen
dc.subjectPreconditioningen
dc.subjectSchur complement approximationen
dc.titleFast Solvers for Cahn--Hilliard Inpaintingen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Imaging Sciencesen
dc.contributor.institutionMax Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germanyen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.