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SUMMARY:A fractional inpainting model based on the vector-valued Cahn-Hill
 iard equation - Jessica Bosch (Max Planck Institute for Dynamics of Comple
 x Technical Systems)
DTSTART:20160113T160000Z
DTEND:20160113T170000Z
UID:TALK63149@talks.cam.ac.uk
CONTACT:Mr Simone Parisotto
DESCRIPTION:The Cahn-Hilliard equation provides a simple and fast tool for
  binary image inpainting. By now\, two generalizations to gray value image
 s exist: Bitwise binary inpainting and TV-H^-1 inpainting. This paper outl
 ines a model based on the vector-valued Cahn-Hilliard equation. Additional
 ly\, we generalize our approach to a fractional-in-space version. In doing
  so\, we replace the standard differential operator by a corresponding fra
 ctional differential operator. Fourier spectral methods provide efficient 
 solvers since they yield a fully diagonal scheme. Furthermore\, their appl
 ication to three spatial dimensions is straightforward. Numerical examples
  show the superiority of the fractional approach over the classical one. I
 t improves the peak signal-to-noise ratio and structural similarity index.
  Likewise\, the experiments confirm that the proposed model competes with 
 previous inpainting methods\, such as the total variation inpainting appro
 ach and its fourth-order variant.
LOCATION:MR14\, Centre for Mathematical Sciences
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