Source Conditions for non-quadratic Tikhonov Regularisation

2020/02/21 by Markus Grasmair, Grasmair, Markus
Mathematics · Engineering · Computer Science · #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2002.09336

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 Hölder type convergence rates known from classical theory.

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