The Inverse Born Approximation: Exact Determination of Shape of Convex Voids

The Inverse Born Approximation (IBA) to the elastic wave inverse scattering problem is known to give highly accurate results for the shape of complex voids. In this paper we present an argument demonstrating that the IBA is, in fact, exact for determining the size, shape and orientation of a wide class of these scatterers given infinite bandwidth and unlimited aperture information. Essentially, our argument demonstrates how the IBA algorithm picks out the singular contribution to the impulse response function and correctly relates it to the shape of the scatterer. Some specific examples will be used to illustrate the more intuitive aspects of the discussion