Morozov's discrepancy principle for Tikhonov-type functionals with nonlinear operators

In this paper we deal with Morozov's discrepancy principle as an a posteriori parameter choice rule for Tikhonov regularization with general convex penalty terms *V for nonlinear inverse problems. It is shown that a regularization parameter *a fulfilling the discprepancy principle exists, whenever the operator F satisfies some basic conditions, and that for suitable penalty terms the regularized solutions converge to the true solution in the topology induced by *V. It is illustrated that for this parameter choice rule it holds *a -> 0, *dq/*a -> 0 as the noise level *d goes to 0. Finally, we establish convergence rates with respect to the generalized Bregman distance and a numerical example is presented.