Reconstruction for shape and impedance in an inverse scattering problem

Abstract

In this paper, we consider an inverse scattering problem of reconstructing the shape and impedance for a cavity from one point source and several measurements placed on a curve inside the cavity. This inverse problem is nonlinear and ill-posed. To overcome such difficulties, we apply an iterative regularized approach to reconstruct both the boundary and the surface impedance, and prove injectivity for the linearized system at the exact solution. Finally, some numerical experiments are presented to demonstrate the feasibility and effectiveness of the proposed regularization method.

Keywords:

• Inverse problem
• shape reconstruction
• impedance reconstruction
• ill-posed problem
• iterative regularization

2010 AMS SUBJECT CLASSIFICATIONS:

• 35R30
• 49N45
• 65M32
• 65N20

Acknowledgments

The authors would like to thank the referees for their valuable comments and suggestions which helped improve our manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of H.H. Qin was supported in part by the NNSF of China under grants 11501562 and the Fundamental Research Funds for the Central Universities 2015QNA49. The research of H.K. Pang was supported by the NNSF of China under grants 11771189, the Natural Science Foundation of Jiangsu Province under grants BK20171162 and the Qing-Lan Project of Jiangsu Province. The research of J.C. Liu was supported in part by the NNSF of China under grants 11601512.