Iterative region-of-interest reconstruction from limited data using prior information

In practice, computed tomography and computed laminography applications suffer from incomplete data. In particular, when inspecting large objects with extremely different diameters in longitudinal and transversal directions or when high resolution reconstructions are desired, the physical conditions of the scanning system lead to restricted data and truncated projections, also known as the interior or region-of-interest (ROI) problem. To recover the searched-for density function of the inspected object, we derive a semi-discrete model of the ROI problem that inherently allows the incorporation of geometrical prior information in an abstract Hilbert space setting for bounded linear operators. Assuming that the attenuation inside the object is approximately constant, as for fibre reinforced plastics parts or homogeneous objects where one is interested in locating defects like cracks or porosities, we apply the semi-discrete Landweber–Kaczmarz method to recover the inner structure of the object inside the ROI from the measured data resulting in a semi-discrete iteration method. Finally, numerical experiments for three-dimensional tomographic applications with both an inherent restricted source and ROI problem are provided to verify the proposed method for the ROI reconstruction