Tikhonov Regularization for Finitely and Infinitely Smoothing Operators

Source abstract

The main goal of this paper is to obtain a unified theory of Tikhonov regularization, incorporating explicit asymptotic rates of convergence based on a priori assumptions, which cover both the finitely and infinitely smoothing forward operators, and to extend a classic result of Natterer to this more general framework. More specifically, it is shown that, for a large class of operators, as in the finitely smoothing case obtained by Natterer, the stabilizing functional involved in the minimization process can be determined by larger norms over much smaller classes than those determined by the a priori assumption for the true solution.