MOROZOV'S DISCREPANCY PRINCIPLE FOR TIKHONOV-REGULARIZATION OF NONLINEAR OPERATORS

Abstract

ABSTRACT We consider Morozov's discrepancy principle for Tikhonov-regularization of nonlinear operator equations. It is shown that minor restrictions to the operator F and the solution x* of the equation already guarantee the existence of a regularization parameter α such that holds, and a convergence rate result is given. Finally we investigate some practically relevant examples, e.g., medical imaging (Single Photon Emission Computed Tomography). It is illustrated that the introduced conditions on F will be met in general by a large class of nonlinear operators. Acknowledgments