On Tikhonov Functionals Penalized by Bregman Distances

Ismael Bleyer; A. Leitão

Authors

Ismael Bleyer Department of Mathematics, Federal University of St. Catarina, P.O. Box 476, 88040-900, Florianópolis, Brazil.
A. Leitão Department of Mathematics, Federal University of St. Catarina, P.O. Box 476, 88040-900, Florianópolis, Brazil.

Keywords:

Tikhonov functionals, Bregman distances, Total variation regularization

Abstract

We investigate Tikhonov regularization methods for linear and nonlinear ill-posed problems in Banach spaces, where the penalty term is described by Bregman distances. We prove convergence and stability results. Moreover, using appropriate source conditions, we are able to derive rates of convergence in terms of Bregman distances. We also analyze an iterated Tikhonov method for nonlinear problems, where the penalization is given by an appropriate convex functional.