An entropic Landweber method for linear ill-posed problems

Burger M, Resmerita E, Benning M (2020)

Publication Type: Journal article

Publication year: 2020


Book Volume: 36

Article Number: 015009

Journal Issue: 1

DOI: 10.1088/1361-6420/ab5c49


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.

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Burger, M., Resmerita, E., & Benning, M. (2020). An entropic Landweber method for linear ill-posed problems. Inverse Problems, 36(1).


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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