LAUSR

This article concerns an extension of the topological derivative concept for 3D inverse acoustic scattering problems involving the identification of penetrable obstacles, whereby the featured data-misfit cost function \begin{document} $\mathbb{J}$ \end{document} is expanded in powers of the characteristic radius \begin{document} $a$ \end{document} of a single small inhomogeneity. The \begin{document} $O(a^6)$ \end{document} approximation \begin{document} $\mathbb{J}_6$ \end{document} of \begin{document} $\mathbb{J}$ \end{document} is derived and justified for a single obstacle of given location, shape and material properties embedded in a 3D acoustic medium of arbitrary shape. The generalization of \begin{document} $\mathbb{J}_6$ \end{document} to multiple small obstacles is outlined. Simpler and more explicit expressions of \begin{document} $\mathbb{J}_6$ \end{document} are obtained when the scatterer is centrally-symmetric or spherical. An approximate and computationally light global search procedure, where the location and size of the unknown object are estimated by minimizing \begin{document} $\mathbb{J}_6$ \end{document} over a search grid, is proposed and demonstrated on numerical experiments, where the identification from known acoustic pressure on the surface of a penetrable scatterer embedded in a acoustic semi-infinite medium, and whose shape may differ from that of the trial obstacle assumed in the expansion of \begin{document} $\mathbb{J}$ \end{document} , is considered.