Spectral Approximation of Fractional PDEs in Image Processing and Phase Field Modeling

Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets and sharp transitions across interfaces are of interest. The...

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Veröffentlicht in:Journal of computational methods in applied mathematics Jg. 17; H. 4; S. 661 - 678
Hauptverfasser: Antil, Harbir, Bartels, Sören
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Minsk De Gruyter 01.10.2017
Walter de Gruyter GmbH
Schlagworte:
26A33
35S15
49K20
49M05
65N12
65N35
65R20
Differential equations
Error Analysis
Fourier Spectral Method
Fractional Laplacian
Image Denoising
Image processing
Mathematical analysis
Mathematical models
Operators (mathematics)
Phase Field Models
ISSN:1609-4840, 1609-9389
Online-Zugang:Volltext
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Abstract Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets and sharp transitions across interfaces are of interest. The numerical solution of corresponding model problems via a spectral method is analyzed. Its efficiency and features of the model problems are illustrated by numerical experiments.
AbstractList Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets and sharp transitions across interfaces are of interest. The numerical solution of corresponding model problems via a spectral method is analyzed. Its efficiency and features of the model problems are illustrated by numerical experiments.
Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets and sharp transitions across interfaces are of interest. The numerical solution of corresponding model problems via a spectral method is analyzed. Its efficiency and features of the model problems are illustrated by numerical experiments.
Author Bartels, Sören
Antil, Harbir
Author_xml – sequence: 1
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  surname: Antil
  fullname: Antil, Harbir
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  givenname: Sören
  surname: Bartels
  fullname: Bartels, Sören
  email: bartels@mathematik.uni-freiburg.de
  organization: Department of Applied Mathematics, Mathematical Institute, University of Freiburg, Hermann-Herder-Str. 9, 79104 Freiburg im Breisgau, Germany
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Snippet Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image...
Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image...
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walterdegruyter
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StartPage 661
SubjectTerms 26A33
35S15
49K20
49M05
65N12
65N35
65R20
Differential equations
Error Analysis
Fourier Spectral Method
Fractional Laplacian
Image Denoising
Image processing
Mathematical analysis
Mathematical models
Operators (mathematics)
Phase Field Models
Title Spectral Approximation of Fractional PDEs in Image Processing and Phase Field Modeling
URI https://www.degruyter.com/doi/10.1515/cmam-2017-0039
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Volume 17
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