Direct sampling method for solving the inverse acoustic wave scattering problems in the time domain

Based on the direct sampling method, this paper solves the inverse acoustic wave scattering problem from the transient scattered field. Two indicator functions can be obtained to reconstruct the shapes and the locations of the unknown scatterers, including the point-like scatterers and the extended scatterers. Our reconstruction method is easy to be implement because only the integrals need to be computed for the indicator functions. The asymptotic properties of the indicator function for the point-like scatterer are proved according to the Fourier-Laplace transform. Meanwhile, the effectiveness and the robustness of our method have been illustrated from two numerical examples.