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

被引：54
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
收藏
页码：661 / 678
页数：18
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