Reconstruction of a penetrable cavity and the external obstacle

Abstract

The inverse acoustic scattering of point sources by a penetrable cavity and the external obstacle is considered. Making use of the internal measurements of scattered field on a closed curve inside the cavity, we first derive a factorization method which provides a rigorous characterization of the support of the cavity without knowing the external object. Then under the condition of the cavity is known in advance, we show that the linear sampling method can be applied to recover the outside obstacle with the help of some Green function.

Keywords:

• Inverse scattering
• penetrable cavity
• the factorization method
• the linear sampling method

AMS Subject Classification:

• 34L25

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper is supported by National Natural Science Foundation of People’s Republic of China [grant number 11571132], [grant number 11601138]; the Fundamental Research Funds for South-Central University for Nationalities [grant number CZY16008].