An entropic Landweber method for linear ill-posed problems

Burger M, Resmerita E, Benning M (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Inverse Problems Institute of Physics: Hybrid Open Access

Book Volume: 36

Article Number: 015009

Journal Issue: 1

DOI: 10.1088/1361-6420/ab5c49

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.

Authors with CRIS profile

Martin Burger Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Alpen-Adria-Universität Klagenfurt AT Austria (AT) Queen Mary University of London GB United Kingdom (GB)

How to cite

APA:

Burger, M., Resmerita, E., & Benning, M. (2020). An entropic Landweber method for linear ill-posed problems. Inverse Problems, 36(1). https://doi.org/10.1088/1361-6420/ab5c49

MLA:

Burger, Martin, E. Resmerita, and M. Benning. "An entropic Landweber method for linear ill-posed problems." Inverse Problems 36.1 (2020).

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