# A direct variational approach to a problem arising in image reconstruction

created on 14 May 2002
modified on 17 Dec 2002

[BibTeX]

Accepted Paper

Inserted: 14 may 2002
Last Updated: 17 dec 2002

Journal: Interfaces and Free Boundaries
Year: 2002

Abstract:

We consider a variational approach to the problem of recovering a missing or damaged part of an image. Representing the (grey) image by a scalar function $u$, the energy to be minimized is $$\int \nabla u {\rm div\,}\left(\frac{\nabla u}{ \nabla u }\right)p\,dx$$ This energy takes into account the perimeter and the $L^p$ norm of the mean curvature of the level sets of $u$.