The concept of topological sensitivity has been successfully employed as an imaging tool to obtain the correct initial topology and preliminary geometry of hidden obstacles for a variety of inverse scattering problems. In this paper, we extend these ideas to acoustic scattering involving transient waveforms and penetrable obstacles. Through a boundary integral equation framework, we present a derivation of the topological sensitivity for the featured class of problems and illustrate numerically the utility of the proposed method for preliminary geometric reconstruction of penetrable obstacles. For generality, we also cast the topological sensitivity in the so-called adjoint field setting that is amenable to a generic computational treatment using, for example, finite element or finite difference methods.
Bibliographical noteFunding Information:
This work was supported, in part, by the Office of Science (BER), U.S. Department of Energy ( DE-SC0008397 ), and NCI of Cancer Nanotechnology Excellence Grant CCNE-TR U54 CA119367 , CA151459 .
- Acoustic waves
- Inverse scattering
- Topological derivative
- Transient waveforms