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

被引：55

作者：

Antil, Harbir ^{[1
]}

Bartels, Soeren ^{[2
]}

机构：

[1] George Mason Univ, Dept Math Sci, Fairfax, VA 22030 USA

[2] Univ Freiburg, Math Inst, Dept Appl Math, Hermann Herder Str 9, D-79104 Freiburg, Germany

来源：

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS | 2017年 / 17卷 / 04期

基金：

美国国家科学基金会;

关键词：

Fractional Laplacian; Image Denoising; Phase Field Models; Error Analysis; Fourier Spectral Method; CAHN-HILLIARD EQUATION; BOUNDED VARIATION; FINITE-ELEMENTS; NOISE REMOVAL; BESOV-SPACES; ALLEN-CAHN; CONVERGENCE; REGULARIZATION; MINIMIZATION; ALGORITHMS;

D O I：

10.1515/cmam-2017-0039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：661 / 678

页数：18

共 43 条

[1] ANALYSIS AND APPROXIMATION OF A FRACTIONAL CAHN-HILLIARD EQUATION [J].

Ainsworth, Mark ;

Mao, Zhiping .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2017, 55 (04) :1689-1718

[2]

Antil H., 2017, PREPRINT

[3] A NOTE ON SEMILINEAR FRACTIONAL ELLIPTIC EQUATION: ANALYSIS AND DISCRETIZATION [J].

Antil, Harbir ;

Pfefferer, Johannes ;

Warma, Mahamadi .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2017, 51 (06) :2049-2067

[4] Regularization in Sobolev Spaces with Fractional Order [J].

Assmann, U. ;

Roesch, A. .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2015, 36 (03) :271-286

[5]

Bartels S., 2015, Numerical Methods for Nonlinear Partial Differential Equations, V47

[6] Broken Sobolev space iteration for total variation regularized minimization problems [J].

Bartels, Soeren .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2016, 36 (02) :493-502

[7] TOTAL VARIATION MINIMIZATION WITH FINITE ELEMENTS: CONVERGENCE AND ITERATIVE SOLUTION [J].

Bartels, Soeren .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2012, 50 (03) :1162-1180

[8] ROBUST A PRIORI AND A POSTERIORI ERROR ANALYSIS FOR THE APPROXIMATION OF ALLEN-CAHN AND GINZBURG-LANDAU EQUATIONS PAST TOPOLOGICAL CHANGES [J].

Bartels, Soeren ;

Mueller, Ruediger ;

Ortner, Christoph .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2011, 49 (01) :110-134

[9] AN IMPLICIT MIDPOINT SPECTRAL APPROXIMATION OF NONLOCAL CAHN-HILLIARD EQUATIONS [J].

Benesova, Barbora ;

Melcher, Christof ;

Sueli, Endre .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2014, 52 (03) :1466-1496

[10] Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization [J].

Bueno-Orovio, Alfonso ;

Kay, David ;

Grau, Vicente ;

Rodriguez, Blanca ;

Burrage, Kevin .

JOURNAL OF THE ROYAL SOCIETY INTERFACE, 2014, 11 (97)

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