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

• 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

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...