A markovian regularization approach of the Modified Gradient Method for solving a two-dimensional inverse scattering problem

In this paper, we consider a two-dimensional inverse scattering problem dealing with microwave tomograpky. To solve this non-linear and ill-posed problem, an iterative scheme based on the Modified Gradient Method (MGM) is used. A Bayesian estimation framework was chosen to build up a regularization scheme based on the weak membrane model. The object to be retrieved being represented by a complex function, two energy terms acting separately on the real and imaginary parts were considered. Consequently, some modifications of the MGM were done. The resulting algorithm is tested against microwave lab oratory-controlled data.