ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

Handle URI:
http://hdl.handle.net/10754/597463
Title:
ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing
Authors:
Calatroni, Luca; Düring, Bertram; Schönlieb, Carola-Bibiane
Abstract:
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.
Citation:
Calatroni L, Düring B, Schönlieb C-B (2013) ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing. DCDS-A 34: 931–957. Available: http://dx.doi.org/10.3934/dcds.2014.34.931.
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Discrete and Continuous Dynamical Systems
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
Aug-2013
DOI:
10.3934/dcds.2014.34.931
Type:
Article
ISSN:
1078-0947
Sponsors:
Carola-Bibiane Schonlieb acknowledges the financial support provided by the Cambridge Centre for Analysis (CCA), the Royal Society International Exchanges Award IE110314 for the project High-order Compressed Sensing for Medical Imaging, the EPSRC first grant Nr. EP/J009539/1 Sparse & Higher-order Image Restoration, and the EPSRC / Isaac Newton Trust Small Grant on Non-smooth geometric reconstruction for high resolution MRI imaging of fluid transport in bed reactors. Further, this publication is based on work supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorCalatroni, Lucaen
dc.contributor.authorDüring, Bertramen
dc.contributor.authorSchönlieb, Carola-Bibianeen
dc.date.accessioned2016-02-25T12:40:13Zen
dc.date.available2016-02-25T12:40:13Zen
dc.date.issued2013-08en
dc.identifier.citationCalatroni L, Düring B, Schönlieb C-B (2013) ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing. DCDS-A 34: 931–957. Available: http://dx.doi.org/10.3934/dcds.2014.34.931.en
dc.identifier.issn1078-0947en
dc.identifier.doi10.3934/dcds.2014.34.931en
dc.identifier.urihttp://hdl.handle.net/10754/597463en
dc.description.abstractWe present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.en
dc.description.sponsorshipCarola-Bibiane Schonlieb acknowledges the financial support provided by the Cambridge Centre for Analysis (CCA), the Royal Society International Exchanges Award IE110314 for the project High-order Compressed Sensing for Medical Imaging, the EPSRC first grant Nr. EP/J009539/1 Sparse & Higher-order Image Restoration, and the EPSRC / Isaac Newton Trust Small Grant on Non-smooth geometric reconstruction for high resolution MRI imaging of fluid transport in bed reactors. Further, this publication is based on work supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.subjectADI splittingen
dc.subjectHigher-order nonlinear diffusionen
dc.subjectImage processingen
dc.subjectTotal variationen
dc.titleADI splitting schemes for a fourth-order nonlinear partial differential equation from image processingen
dc.typeArticleen
dc.identifier.journalDiscrete and Continuous Dynamical Systemsen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
dc.contributor.institutionUniversity of Sussex, Sussex, United Kingdomen
kaust.grant.numberKUK-I1-007-43en
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