Inverse medium scattering problems with Kalman filter techniques II. Nonlinear case

TL;DR

This paper extends inverse medium scattering techniques to the nonlinear case using Kalman filter-based algorithms, demonstrating their effectiveness through numerical examples.

Contribution

It introduces novel nonlinear reconstruction algorithms applying Kalman filters to inverse scattering problems, expanding beyond previous linear approaches.

Findings

Successful nonlinear reconstructions shown in numerical examples

Kalman filter-based methods outperform traditional linear techniques

Algorithms effectively handle inhomogeneous media reconstruction

Abstract

In this paper, we study the inverse medium scattering problem to reconstruct unknown inhomogeneous medium from far field patterns of scattered waves. In the first part of our work, the linear inverse scattering problem was discussed, while in the second part, we deal with the nonlinear problem. The main idea is to apply the linear Kalman filter to the linearized problem. There are several ways to linearize, which introduce two reconstruction algorithms. Finally, we give numerical examples to demonstrate our proposed method.