Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - S. Masnou

A direct variational approach to a problem arising in image reconstruction

created on 14 May 2002
modified on 17 Dec 2002


Accepted Paper

Inserted: 14 may 2002
Last Updated: 17 dec 2002

Journal: Interfaces and Free Boundaries
Year: 2002


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 $u$.


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