Bayesian estimation with Gauss-Markov-Potts priors in optical diffraction tomography

In this paper, Optical Diffraction Tomography (ODT) is considered as an inverse scattering problem. The goal is to retrieve a map of the electromagnetic parameters of an unknown object from measurements of the scattered electric field that results from its interaction with a known interrogating wave. This is done in a Bayesian estimation framework. A Gauss-Markov-Potts prior appropriately translates the a priori knowledge that the object is made of a finite number of homogeneous materials distributed in compact homogeneous regions. 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. Some preliminary results, obtained by applying the inversion algorithm to experimental laboratory controlled data, will illustrate the performances of the proposed method that is compared to the more classical Contrast Source Inversion method (CSI) developed in a deterministic framework.