Results on mixed anisotropic L2-BV regularization of Ill-posed problems and applications to image restoration.

MAZZIERI, GISELA L; SPIES, RUBÉN D; TEMPERINI, KARINA G

Beijing

Congreso; 8th International Congress on Industrial and Applied Mathematics, ICIAM 2015; 2015

Several generalizations of the traditional Tikhonov-Phillips regularization method for inverse ill-posed problems have been proposed during the last decades. Many of these variants consists essentially in modifications of the penalizing term, which forces certain features in the obtained regularized solution. If it is known that the regularity of the exact solution is inhomogeneous it is often desirable the use of mixed, dpatially adaptive methods. These methods are also highly suitable when the reservation of borders and edges is also an important issue, since they allow for the inclusion of penalizers appropriate for border detection. In this work, we propose the use of a convex spatially-adaptive combination of classic L2 penalizers and anisotropic bounded variation semi-norm. Results on existence and uniqueness of minimizers of the corresponding Tikhonov-Phillips functional are presented. Stability results of those minimizers with respect to different perturbations are presented and applications to image restoration problems are shown.