Microwave imaging within the second-order Born approximation: stochastic optimization by a genetic algorithm

This paper addresses the problem of reconstructing the location, shape, and dielectric permittivity distribution of an inhomogeneous dielectric object from measurements of the field scattered by the object. The object is an inhomogeneous infinite cylinder of arbitrary cross section illuminated by a transverse magnetic incident electric field. The approach is based on the Lippmann-Schuringer integral equation for the electromagnetic inverse scattering problem, approximated by applying the second-order Born approximation, which allows an extension of the range of contrast values that can be accurately imaged. The numerical approach is developed in the spatial domain and makes use of a multi-illumination multiview processing. In particular, the inverse problem is recast in a global nonlinear optimization problem (including a penalty function), solved by a stochastic method based on a genetic algorithm. In this paper, the mathematical formulation of the approach is described and the results of several dielectric reconstructions are reported, including comparisons with analogous reconstructions performed within the linearized (first-order) Born approximation.