THE RECONSTRUCTION OF THE SURFACE OF SCATTERERS WITH CONTINUOUS CURVATURE VIA LOW-FREQUENCY MOMENTS

In this work, the reconstruction of the shape of an acoustically soft scatterer from knowledge of the scattering amplitude is examined. It is demonstrated that if we work in the low-frequency region and the scatterer's surface is assumed to have continuous curvature then we can construct polynomial surfaces tending to coincide with the scatterer's surface as their degree increases. The proposed method is stable in such a way that small measurement errors lead to small changes of the polynomial surfaces approximating the scatterer's surface.