Inverse medium scattering problems with Kalman filter techniques I. Linear case

TL;DR

This paper introduces a Kalman filter-based method for solving linear inverse acoustic scattering problems, enabling sequential estimation of unknown media and demonstrating equivalence to Tikhonov regularization with numerical validation.

Contribution

It presents a novel Kalman filter approach for linear inverse scattering problems, linking it to Tikhonov regularization and providing numerical demonstrations.

Findings

Kalman filter estimates are equivalent to Tikhonov regularization in linear cases

The method allows sequential reconstruction of inhomogeneous media

Numerical examples validate the effectiveness of the approach

Abstract

In this paper, we study the inverse acoustic medium scattering problem to reconstruct the unknown inhomogeneous medium from far field patterns of scattered waves. We propose the reconstruction scheme based on the Kalman filter, which becomes possible to sequentially estimate the inhomogeneous medium. We also show that in the linear inverse problem, the estimation for the Kalman filter is equivalent to that for the Tikhonov regularization. Finally, we give numerical examples to demonstrate our proposed method.