An Application of Source Inequalities for Convergence Rates of Tikhonov Regularization with a Non-differentiable Operator

Abstract

In this paper we study Tikhonov regularization for the stable solution of an ill-posed non-linear operator equation. The operator we consider, which is related to an active contour model for image segmentation, is continuous, compact, but nowhere differentiable. Nevertheless we are able to derive convergence rates under different smoothness assumptions on the true solution by employing the method of variational or source inequalities. With this approach, we can prove up to linear convergence with respect to the norm.