Inverse scattering from experimental microwave data using the weak membrane model and a positivity constraint

The goal of microwave inverse scattering is to reconstruct the permittivity distribution of an object from measured scattered field data. In order to solve this nonlinear and ill-posed problem, an iterative scheme based on the minimization of a cost functional is considered. In order to enhance the reconstruction quality when trying to reconstruct objects with large contrast values or working with experimental data, a priori knowledge on the reconstructed object can be added within the scheme. The considered regularized scheme is introduced within a Bayesian estimation framework. A cost functional, combining a quadratic data fitting term with a positivity constraint in the maximum entropy sense and a weak membrane model, is proposed. To minimize the considered criterion, a deterministic relaxation algorithm based on the graduated non convexity (GNC) principle has been applied. Although the convergence of this algorithm cannot be rigorously demonstrated, it has been shown to be effective in reconstructing a variety of inhomogeneous objects from simulated data.