An entropic Landweber method for linear ill-posed problems. (19th December 2019)

• Record Type: Journal Article
• Authors: Burger, M; Resmerita, E; Benning, M
• Is Part Of: Inverse problems. Volume 36:Number 1(2020)
• Publication Date: 2019-12-19
• Subjects: regularization -- Shannon entropy -- Landweber method -- integral equation; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab5c49
• Languages: English
• ISSNs: 0266-5611

Abstract

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.