A fast method for acoustic imaging of multiple three-dimensional objects

This paper is concerned with the inverse problem for imaging multiple three-dimensional objects using the information of the far-field pattern of the scattered wave. A spatially dependent function, which has noticeably different values inside and outside the obstacle, is derived. A numerical method based on the characterization is developed to obtain a visualization of the obstacle. The most remarkable advantage of this method is that it does not need any prior knowledge about the geometry and physical properties of the scatterer, and requires only the information of the far-field measurements for a finite number of directions of incidence and observation distributed over a limited range. Furthermore, the scheme is very simple and fast since it avoids the use of the iterative procedure and requires only the solution of a linear system. Some numerical examples with synthetic far-field data are given showing the practicality and efficiency of this scheme.