Daniel Gerth: Tikhonov regularization with oversmoothing penalties

Author(s):

Daniel Gerth

Title:

Daniel Gerth: Tikhonov regularization with oversmoothing penalties

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 08, 2016

Mathematics Subject Classification:

    65J20 []
    47A52 []

Abstract:

In the last decade l1-regularization became a powerful and popular tool for the regularization of Inverse Problems. While in the early years sparse solution were in the focus of research, recently also the case that the coefficients of the exact solution decay sufficiently fast was under consideration. In this paper we seek to show that -regularization is applicable and leads to optimal convergence rates even when the exact solution does not belong to l1 but only to l2. This is a particular example of over- smoothing regularization, i.e., the penalty implies smoothness properties the exact solution does not fulfill. We will make some statements on convergence also in this general context.

Keywords:

Tikhonov regularization, convergence rates, l1-regularization, oversmoothing

Language:

English

Publication time:

12/2016