# An entropic Landweber method for linear ill-posed problems

## TL;DR

This paper introduces an entropic Landweber iterative method for regularizing linear ill-posed problems, providing a closed-form solution, convergence analysis, and numerical validation for reconstructing nonnegative unknowns and probability distributions.

## Contribution

It presents a novel entropic projection approach with explicit iterates and analyzes its convergence, extending the Landweber method for specific applications.

## Key findings

- Effective in reconstructing nonnegative unknowns
- Converges reliably in numerical experiments
- Relates to and extends existing methods

## Abstract

The aim of this paper is to investigate the use of an entropic projection method for the iterative 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.