The linear sampling method in a waveguide: a modal formulation

Abstract

This paper concerns the linear sampling method used to retrieve obstacles in a 2D or 3D acoustic waveguide. The classical mathematical results concerning the identifiability of the obstacle and the justification of the inverse method are established for this particular geometry. Our main concern is to derive a modal formulation of the linear sampling method that is well adapted to the waveguide configuration. In particular, thanks to such formulation, we highlight the fact that finding some obstacles from remote scattering data is more delicate in a waveguide than in free space. Indeed, the presence of evanescent modes increases the ill posedness of the inverse problem. However, we show that the numerical reconstruction of obstacles by using the far field is feasible, even by using a few incident waves.