A Recursive Born Approach to Nonlinear Inverse Scattering
  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. 
Ulugbek S. Kamilov, Dehong Liu, Hassan Mansour, and Petros T.   Boufounos
cs.LG physics.optics