Limited Projection 3D X-Ray Tomography Using the Maximum Entropy Method

It is well known from physics that the reconstruction of physical quantities from experimental data is often obstructed by incomplete information, the presence of noise and the ill-posed nature of the inversion problem. It was shown [1] that a Bayesian reconstruction (BR) in terms of the Maximum Entropy Method (MEM) combined with unbiased a priori knowledge, if available, is one way to overcome the difficulties. Similar problems occur while extracting useful information from incomplete data sets in technical applications. The solution of the deduced iteration procedure, if converged, gives the most probable one among all possible solutions. In case of radiographic techniques difficulties occur if there is no free access around the object or if the number of available radiographic projections is limited due to other reasons like restricted maximum exposure as often required for medical applications or economical aspects. This situation, characterized by a significant lack of data, makes it impossible to apply reconstruction algorithms which are usually used for computer tomography (CT). Other reconstruction algorithms can be found by introducing prior information (compare [1–6]) about the object and the structures of interest. Those algorithms meet practical requirements like robustness, reduction of experimental and numerical effort, or others. For NDE applications, e.g. the inspection of welds or castings, prior knowledge can be introduced from a practical point of view by assuming a binary or multi-material structure. This reduces significantly the number of permissible solutions and therefore the number of required radiographie projections.</p