Inverse scattering solutions of scalar Helmholtz wave equation by a multiple source moment method

Abstract

Determining the spatial scattering function, i.e. solving the inverse scattering problem, with the Helmholtz wave equation model is known to be an ill posed problem for a single incident radiation field. We show that the problem becomes well posed if formulated as seeking the common scattering function which produces a best prediction of the given scattering data for sufficiently many sources and receivers. The scattering function is found by solution of a system of non-linear algebraic equations which are derived by the method of moments. Our method avoids perturbation theory approximations.