Regularization of systems of nonlinear ill-posed equations: II. Applications

TL;DR

This paper applies modified Landweber-Kaczmarz methods to three nonlinear inverse problems, demonstrating their robustness, stability, efficiency, and high accuracy in practical applications like thermoacoustic tomography and semiconductor equations.

Contribution

It extends the previous convergence analysis to three new nonlinear inverse problems, showcasing the effectiveness of the algorithms in diverse real-world scenarios.

Findings

Algorithms are robust and stable across applications.

High accuracy achieved in inverse problem solutions.

Computational efficiency demonstrated in practical cases.

Abstract

In part I we introduced modified Landweber-Kaczmarz methods and have established a convergence analysis. In the present work we investigate three applications: an inverse problem related to thermoacoustic tomography, a nonlinear inverse problem for semiconductor equations, and a nonlinear problem in Schlieren tomography. Each application is considered in the framework established in the previous part. The novel algorithms show robustness, stability, computational efficiency and high accuracy.