Work

An entropic Landweber method for linear ill-posed problems

Year: 2019

Type: article

Abstract: The aim of this paper is to investigate the use of a Landweber-type method involving the Shannon entropy for the regularization of linear ill-posed problems. We derive a closed form solution for the iterates and analyze their convergence behaviour both in a case of reconstructing general nonnegative unknowns as well as for the sake of recovering probability distributions. Moreover, we discuss several variants of the algorithm and relations to other methods in the literature. The effectiveness of the approach is studied numerically in several examples.

Source: Inverse Problems

DOI: 10.1088/1361-6420/ab5c49

Authors: M Burger, E Resmerita, M Benning

Institutions: Friedrich-Alexander-Universität Erlangen-Nürnberg, University of Klagenfurt, Queen Mary University of London

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,700

Funders: Leverhulme Trust, European Commission