  The Iterative Born Approximation (IBA) is a well-known method for describing
waves scattered by semi-transparent objects. In this paper, we present a novel
nonlinear inverse scattering method that combines IBA with an edge-preserving
total variation (TV) regularizer. The proposed method is obtained by relating
iterations of IBA to layers of a feedforward neural network and developing a
corresponding error backpropagation algorithm for efficiently estimating the
permittivity of the object. Simulations illustrate that, by accounting for
multiple scattering, the method successfully recovers the permittivity
distribution where the traditional linear inverse scattering fails.
