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.

This presentation is part of Minisymposium “MS55 - Advances of regularization techniques in iterative reconstruction (2 parts)”
organized by: Zichao (Wendy) Di (Argonne National Lab) , Marc Aurèle Gilles (Cornell University) .

Authors:

Harbir Antil (George Mason University)

Keywords:

image deblurring, image reconstruction, image segmentation, integral equations for image analysis, nonlinear optimization, partial differential equation models