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Hierarchical Markovian models for 3D Computed Tomography in non destructive testing applications

So as to detect and characterize potential defects in pipes, inspections are carried out with the help of non-destructive examination techniques (NDE) including X-or radiography. Should a defect be detected, one can be asked to prove the component still stands the mechanical constraints. In these cases of expertise, the use of a 3-D reconstruction processing technique can be very useful. One characteristic of such applications is that, in general the number and angles of projections are very limited and the data are very noisy, so the problem is severely ill posed. Hopefully, in these applications we know a priori the number and the types of materials in the object under the study and this is a great piece of prior information. In this work, we first propose a particular hierarchical Markov-Potts a priori model which takes into account for the specificity of the Non Destructive Technique (NDT) Computed Tomography (CT). Then, we give details of a Bayesian estimation computation based on MCMC and EM techniques. Finally, we show the performances of the proposed 3D CT reconstruction method with a very limited number and angles of projections and very low signal to noise ratio simulating from simulating data. These data have been obtained from very simple defects (cubic form) with acquisition conditions that are supposed to be representatives of real inspection in power plants.