Source Conditions for non-quadratic Tikhonov Regularisation

Abstract: In this paper we consider convex Tikhonov regularisation for the solution of linear operator equations on Hilbert spaces. We show that standard fractional source conditions can be employed in order to derive convergence rates in terms of the Bregman distance, assuming some stronger convexity properties of either the regularisation term or its convex conjugate. In the special case of quadratic regularisation, we are able to reproduce the whole range of H\"older type convergence rates known from classical theory.