A generalised diffraction tomography technique based on non-linear optimization and Gaussian basis expansion of the scatterer

A novel method for the nonperturbative solution of the inverse scattering problem is presented. The method is based on the description of the unknown scatterer in terms of Gaussian basis functions and the discretization of the scattering integral equation (SIE) by applying a Gauss quadrature integration procedure. The inverse scattering problem is solved by minimizing the squared error between measured and predicted values for the scattering amplitude, subject to non-linear equality constraints imposed by the SIE for the field in the interior of the scattering object.