RESULTS ON MIXED ANISOTROPIC REGULARIZATION OF INVERSE ILL-POSED PROBLEMS

GISELA MAZZIERI; KARINA TEMPERINI; RUBEN SPIES

Tandil

Congreso; V Congreso de Matemática Aplicada, Computacional e Industrial; 2015

During the last two decades several generalizations of the traditional Tikhonov-Phillips regularization method for solving inverse ill-posed problems have been proposed. Many of these variants consist 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, spatially adaptivemethods. These methods are also highly suitable when the preservation of borders and edges is also an important issue, since they allow for the inclusion of anisotropic penalizers for border detection. In this work, we propose the use of a penalizer resulting from the convex spatially-adaptive combinations of classic penalizing L2 and anisotropic bounded variation (BV) seminorm. Results on existence, uniqueness and stability of minimizers of the corresponding Tikhonov-Phillips functional are presented. An application to image restoration problem is shown.