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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Bibliographic Details
Published in:Journal of computational methods in applied mathematics Vol. 17; no. 4; pp. 661 - 678
Main Authors: Antil, Harbir, Bartels, Sören
Format: Journal Article
Language:English
Published: Minsk De Gruyter 01.10.2017
Walter de Gruyter GmbH
Subjects:
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 Access:Get full text
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Summary: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.
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ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2017-0039