New algorithm for solving variational problems in $W^{1,p}\SO$ and $BV\SO$: Application to image restoration
Résumé
We propose a new unifying method for solving variational problems defined on the Sobolev spaces $W^{1,p}(\Omega)$ or on the space of functions of bounded variations $BV(\Omega)$ ($\Omega\subset\R^N$). The method is based on a recent new characterization of these spaces by Bourgain, Brezis and Mironescu (2001), where norms can be approximated by a sequence of integral operators involving a differential quotient and a suitable sequence of radial mollifiers. We use this characterization to define a variational formulation, for which existence, uniqueness and convergence of the solution is proved. The proposed approximation is valid for any $p$ and does not depend on the attach term. Implementation details are given and we show examples on the image restoration problem.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...