Radu Ioan Bot, Torsten Hein: Iterative regularization with general penalty term - theory and application to $L1$- and $TV$-regularization

Author(s):

Radu Ioan Bot
Torsten Hein

Title:

Iterative regularization with general penalty term - theory and application to $L1$- and $TV$-regularization

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 14, 2011

Mathematics Subject Classification:

47A52	[]
46N10	[]
49N15	[]

Abstract:

In this paper we consider an iterative regularization scheme for linear ill-posed equations in Banach spaces. As opposite to other iterative approaches, we deal with a general penalty functional from Tikhonov regularization and take advantage of the properties of the regularized solutions which where supported by the choice of the specific penalty term. We present convergence and stability results for the presented algorithm. Additionally, we demonstrate how these theoretical results can be applied to $L1$- and $TV$-regularization approaches and close the paper with a short numerical example.

Keywords:

linear ill-posed equations, iterative regularization scheme, s-convex penalty functionals, conjugate functionals

Language:

English

Publication time:

07/2011