Scattering and inverse scattering of sound-hard obstacles via shape deformation

Direct and inverse scattering of plane acoustic waves from sound-hard obstacles are discussed. The direct problem is solved via the application of the Padé approximation. It is shown that this involves solving only certain algebraic recursion relations and requires neither Green's functions nor integral representations of the field. The shape of the scatterer is assumed to be a superposition of a deformation (allowed to be finite) over an underlying simple geometry. It is demonstrated that such a decomposition allows the scattered field to be obtained as solutions of classical Neumann problems in domains exterior to the underlying simple shape instead of the actual deformed contour. This introduces simplifications in the implementation of a Gauss - Newton type inversion procedure which was used in this study. Some inversions of two-dimensional scatterers are presented.