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 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
which is compared to the more classical Contrast Source Inversion method (CSI) developed in a deterministic
framework.
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