The reconstruction of the surface of scatterers with continuous curvature via low-frequency moments

In this work, the reconstruction of the shape of an acousticallysoft scatterer from knowledge of the scattering amplitude isexamined. It is demonstrated that if we work in the low-frequencyregion and the scatterer's surface is assumed to have continuouscurvature then we can construct polynomial surfaces tendingto coincide with the scatterer's surface as their degree increases.The proposed method is stable in such a way that small measurementerrors lead to small changes of the polynomial surfaces approximatingthe scatterer's surface.