Fast acoustic imaging for three dimensional objects in a half-space

An inverse problem aimed to recover the geometrical characteristics of a three dimensional object in the half-space from the knowledge of the far-field pattern of the acoustic scattering waves is investigated. A simply fast method is presented to solve the nonlinear and ill-posed inverse problem. A particular feature of the scheme is that it can reproduce a clear visualization of a three dimensional object in the half space only from the solution of a linear system even when neither the number of components nor the surface boundary condition of each component needs be known a priori.The algorithm has been verified to be considerably efficient by some numerical examples.