The Kirsch-Kress method for inverse scattering by infinite locally rough interfaces

Abstract

This paper is concerned with the inverse problem of reconstructing an infinite, locally rough interface from the scattered field measured on line segments above and below the interface in two dimensions. We extend the Kirsch-Kress method originally developed for inverse obstacle scattering problems to the above inverse transmission problem with unbounded interfaces. To this end, we reformulate our inverse problem as a nonlinear optimization problem with a Tikhonov regularization term. We prove the convergence of the optimization problem when the regularization parameter tends to zero. Finally, numerical experiments are carried out to show the validity of the inversion algorithm.

Keywords:

• Inverse scattering
• Helmholtz equation
• locally rough interface
• transmission problem
• the Kirsch-Kress approach

AMS Subject Classifications:

• 35J05
• 45Q05
• 65R32
• 78A46

Acknowledgements

The authors thank Drs. Jiaqing Yang and Haiwen Zhang for the valuable discussions. The authors also thank the referees for their constructive comments which improved this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partly supported by the NNSF of China [grant number 61379093], [grant number 91430102].