Maria Monserrat Rincon-Camacho: May 5,2011
An adaptive finite element method in L2-TV-based image denoising
Maria Monserrat Rincon-Camacho, University of Graz, Graz, Austria.
Thursday, May 5, 10:30 a.m. in the CERFACS conference room
Abstract:
The first order optimality system of a total variation regularization based variational model with L2-data-fitting in image denoising (L2-TV problem) can be expressed as an elliptic variational inequality of the second kind. For a finite element discretization of the variational inequality problem, an a posteriori error residual based error estimator is derived and its reliability and (partial) efficiency are established. The results are applied to solve the L2-TV problem by means of the adaptive finite element method. The adaptive mesh refinement relies on the newly derived a posteriori error estimator and on an additional local variance estimator to cope with noisy data. The numerical solution of the discrete problem on each level of refinement is obtained by a superlinearly convergent algorithm based on Fenchel-duality and inexact semismooth Newton techniques and which is stable with respect to noise in the data. Numerical results justifying the advantage of adaptive finite elements solutions are presented.
