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

Takashi Furuya; Roland Potthast

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arXiv · 2110.08773

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

Takashi Furuya·Roland Potthast

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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.

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Takashi Furuya, Roland Potthast. 2021-10-17. Inverse medium scattering problems with Kalman filter techniques I. Linear case. https://arxiv.org/abs/2110.08773

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