Gauss-Markov-Potts priors for Bayesian inversion in microwave imaging
Résumé
In this chapter we are concerned with an electromagnetic inverse scattering problem where the goal is to characterize an unknown object from measurements of the field that results from its interaction with a known interrogating wave in the microwave frequency range. The modeling of this interaction is performed by means of an integral representation of the fields in a 2D configuration in the transverse magnetic polarization case. It is well known that the inverse problem is non-linear and ill-posed; it is dealt with by means of an iterative algorithm tailored for objects made of a finite number of different homogeneous dielectric or conductive materials. This means that we introduce, in the inversion algorithm, the a priori information that the image of the contrast that we look for is made of a finite number of homogeneous and compact regions. This a priori information is introduced in the Bayesian estimation framework via a Gauss-Markov random field for the contrast distribution and a hidden Potts-Markov field for the material classes. First, we express the a posteriori distributions of all the unknowns and then a Gibbs sampling algorithm is used to generate samples and estimate the posterior mean of the unknowns.