Bayesian approach with hierarchical Markov modeling for data fusion in image reconstruction applications

In many image reconstruction applications, more and more, we need techniques to combine different kind of data. This is the case, for example, in computed tomography (CT) medical imaging where one may use anatomic atlas data with X ray radiographic data or in non destructive testing (NDT) techniques where one wants to use both gamma rays and ultrasound echo-graphic data. In this paper, First we present the basics of Bayesian estimation approach and will see how the compound or hierarchical Markov modeling will give us the necessary tools for data fusion. Then, we present two examples: one in medical imaging CT application and the second in industrial NDT. In both cases, we consider an X ray CT image reconstruction problem using two different kind of data: classical X-rays radiographic data and some geometrical informations and propose new methods for these data fusion problems. The geometrical information we use are of two kind: partial knowledge of values in some regions and partial knowledge of the edges of some other regions. We show the advantages of using such informations on increasing the quality of reconstructions. We also show some results to analyze the effects of some errors in these data on the reconstruction results.